Linear Algebra and its Applications 413 (2006) 1–12www.elsevier.com/locate/laa

Georg HeinigNovember 24, 1947–May 10, 2005

A personal memoir and appreciationby Karla Rost

doi:10.1016/j.laa.2005.08.022

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On May 10, 2005, Georg Heinig, an excellent mathematician died unexpectedly atthe age of 57. He was a world leader in the field of structured matrices. As associateeditor of the journal Linear Algebra and its Applications since his appointment in1991, he contributed much to the journal’s success by his valuable and extensivework. In what follows, I want to try to capture some aspects of this mathematical lifeand his personality.

Georg was born on November 24, 1947, in the small town of Zschopau in theOre Mountains (Erzgebirge) in East Germany. From 1954 to 1964, he attendedthe elementary school there. Because of his good performance, he was admitted tothe elite school of Karl-Marx-Stadt (now Chemnitz) University of Technology, wherehe received his graduation diploma with the grade “very good”. During his time at thisschool, he already showed extraordinary talent for mathematics and natural sciences,and his passion and skills for solving mathematical problems grew.

Subsequently he studied mathematics at Karl-Marx-Stadt (now Chemnitz) Uni-versity of Technology. He wrote his diploma thesis under the supervision of SiegfriedPrössdorf on some properties of normally solvable operators in Banach spaces. Someyears ago S. Prössdorf told me that he liked to recall the time he spent with the giftedand creative student Georg. In the summer of 1970, Georg received the best possiblegrade for the defense of his diploma thesis.

He received a scholarship to study for the PhD abroad and he decided to go to theState University of Moldavia at Kishinev from 1971 to 1974. There he worked on hisPhD thesis on the subject of Wiener–Hopf block operators and singular integral oper-ators under the supervision of Israel Gohberg [IG] who even then was internationallywell-known and respected.

Here is a copy of the authenticated Russian document certifying Georg’s degreeas “candidate of sciences”, which is the equivalent to a PhD:

A well known, important and often cited work with I. Gohberg from this time isthe paper [111]. With great admiration and deep gratitude Georg always consideredI. Gohberg as his scientific father [IG, p. 63].

By this time, Georg was cast irretrievably into the realm of matrix theory, inparticular the theory of structured matrices. His commitment to this field over threedecades has benefited several scientific grandchildren of Israel Gohberg’s of whom I

K. Rost / Linear Algebra and its Applications 413 (2006) 1–12 3

am one. Georg’s connection to I. Gohberg has never ceased. From 1993 on, he was amember of the editorial board of the journal Integral Equations and Operator Theory.

I became acquainted with Georg when he returned to Karl-Marx-Stadt in late 1974,where he worked at the Department of Mathematics, first in the group chaired by S.Prössdorf and then (after Prössdorf’s leave to Berlin 1975) in B. Silbermann’s group.There he found extremely good conditions. Prössdorf and Silbermann considered himas an equal partner, and hence he could pursue his inclinations in research unhamperedand even build a small research group.

In all honesty, I have to admit that I was not euphoric at my first encounters withGeorg. He was very young, with no experience as a supervisor, and in addition, heappeared to me as too self-oriented. It was his ability to awake my interest in the topicshe proposed, which in 1975 led me to decide to write my diploma thesis under hissupervision despite my initial hesitations. In fact, he turned out to be an extraordinarysupervisor, and I soon became aware that starting my scientific career with him wasa lucky decision. In later years, we managed better and better to get attuned to eachother, and consequently I wrote a large part of my dissertation on the method of UV-reduction for inverting structured matrices under his supervision in 1980. Meanwhile30 years of fruitful and intense joint work have passed. One joint monograph andalmost 40 papers in journals testify to this.

In 1979, Georg defended his habilitation thesis (of an imposing length of 287pages) on the spectral theory of operator bundles and the algebraic theory of finiteToeplitz matrices with excellence.

Georg was very optimistic and in love with life. I very much miss his cheerfuland bright laughter. Certainly, his stay in Kishinev intensified his wanderlust and hiscuriosity for other countries. Despite the travel restrictions for citizens of the GDR,the former socialist part of Germany, there was scientific cooperation with Syria andEthiopia, and Georg was offered a research and working visit at Aleppo University inSyria in 1982. During a longer stay from 1987 to 1989 at Addis Ababa University inEthiopia, he was accompanied by his wife Gerti and by his two children Peter (born1974) and Susanne (born 1977). Later on, both these stays certainly helped him tosettle down in Kuwait.

Georg was well established at Karl-Marx-Stadt (now Chemnitz) University ofTechnology. He was a respected and highly recognized colleague with outstandingachievements in research and teaching. Thus, Georg was appointed as a full professorfor numerical mathematics at Karl Marx University of Leipzig. Since the late seventieshis international recognition has grown enormously, which is, for example, reflectedby the interest of the Birkhäuser publishing house in the joint monograph [85,88],which was originally intended to be published by the Akademie-Verlag only.

The “Wende” in the fall of 1989 was an incisive break and turning point in thelife of many people in East Germany, and thus also for Georg. All scientists workingat universities were formally dismissed and had to apply for a position anew. Animportant criterion for a refusal of such an application was the political proximity tothe old socialist system. Due to this, in 1993 Georg went to Kuwait University, where

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he worked as a professor for more than 10 years. He died of a heart attack on May10, 2005, in his apartment in Kuwait.

During this long period in Kuwait, he continuously maintained scientific and per-sonal contacts with his friends and former colleagues from Chemnitz, including Al-brecht Böttcher, Bernd Silbermann, Steffen Roch, and myself. In May 1998, we allhad the opportunity to participate in the International Conference on Fourier Analysisand Applications in Kuwait. Georg had an especially high admiration for AlbrechtBöttcher and was therefore very glad that Albrecht agreed to enter the scientificcommittee and the editorial board of the proceedings of this conference [33]. In thecourse of that conference, we convinced ourselves with great pleasure of the respectin which Georg was held by his colleagues and students in Kuwait. Thus, he foundvery good friends and supporters in his Kuwaiti colleagues Fadhel Al-Musallam andMansour Al-Zanaidi as well as in his colleague Christian Grossmann from DresdenUniversity of Technology, who stayed in Kuwait from 1992 to 1998. One of thehighlights of his life occurred in 2002, when the Amir of Kuwait distinguished him asthe Researcher of the Year. Since 2004, he was also a member of the editorial boardof the Kuwait Journal of Science and Engineering.

K. Rost / Linear Algebra and its Applications 413 (2006) 1–12 5

My mathematical knowledge and my ability to tackle problems have benefitedimmensely from Georg. He had an extraordinary gift to explain complicated thingsin simple terms. This was also appreciated by his students. His lectures and scientifictalks were very sought after and well attended. The aesthetic component is well tothe fore in his work. He mastered with equal facility problems of extreme generalityand abstraction as well as down-to-earth questions.

Georg is the author and coauthor of more than 100 scientific publications. Healways made high demands on himself and on his coauthors regarding not only math-ematical originality and exactness but also regarding clear and short exposition.

His main research interests are

• structured matrices: algebraic theory and fast algorithms,• interpolation problems,• operator theory and integral equations,• numerical methods for convolution equations,• applications in systems and control theory and signal processing.

In each of these topics, he achieved essential contributions, which is impressivelyshown by his list of publications. In my opinion, especially the importance of hisresults concerning the algebraic theory of structured matrices are striking andimposing. In particular, in our joint paper [74] we show that inverses of matriceswhich are the sum of a Toeplitz and a Hankel matrix possess a Bezoutian structureas inverses of Hankel or Toeplitz matrices do separately. On the basis of thisstructure, for example, matrix representations can be found and fast algorithms canbe designed. Thus, a breakthrough for the class of Toeplitz-plus-Hankel matriceswas achieved.

Moreover, Georg’s observation of the kernel structure of (block) Toeplitz andToeplitz-plus-Hankel matrices turns out to be a suitable key to develop algorithmswithout additional assumptions. His ideas how to connect the structure of a matrixwith its additional symmetries lead to more efficient inversion and solution algorithmsas well as a new kind of factorization. But also his contributions to Toeplitz leastsquare problems, to transformation techniques for Toeplitz and Toeplitz-plus-Hankelmatrices leveraged the research in these fields.

I am proud that he has completed (and still wanted to complete) many mathemat-ical projects with me. For many years, we dreamt about writing a neat textbook onstructured matrices for graduate students, ranging from the basics for beginners upto recent developments. One year ago, we really started writing the first chapters ofthis book. Except for some interruptions, when we were very busy with teaching,the collaboration was therefore especially intense, partly culminating in a dozen ofemails per day. I received two emails from him on May 10, 2005. I then did not knowthat they were his last!

6 K. Rost / Linear Algebra and its Applications 413 (2006) 1–12

Georg’s work leaves behind a trail that points to directions for future research. Hisearly death leaves a loss from which we cannot recover, for it is tragic how many plansand original ideas have passed away with him. Colleagues like me are left behind inshock and ask themselves how we can at least partially close the gap that he has left.

In such situations the persistent optimist Georg used to say:

“Lamenting does not help. Things are as they are.Let us confidently continue to work. This helps!”

References

[BS] A. Böttcher, I. Gohberg, P. Junghanns (Eds.), Toeplitz Matrices and Singular Integral Equations:The Bernd Silbermann Anniversary Volume (Pobershau, 2001), Oper. Theory Adv. Appl., vol. 135,Birkhäuser, Basel, 2002.

[SP] J. Elschner, I. Gohberg, B. Silbermann (Eds.), Oper. Theory Adv. Appl., vol. 121, Birkhäuser, Basel,2001.

[IG] H. Dym, S. Goldberg, M.A. Kaashoek, P. Lancaster (Eds.), The Gohberg Anniversary Collection,vol. I (Calgary, 1988), Oper. Theory Adv. Appl., vol. 40, Birkhäuser, Basel, 1989.

List of Georg Heinig’s (refereed) publications

(Chronologically ordered, including one monography [85,88], two edited proceedings [14,33], and onebook translation [30].)

[1] G. Codevico, G. Heinig, M. Van Barel, A superfast solver for real symmetric Toeplitz systems usingreal trigonometric transformations, Numer. Linear Algebra Appl., in press.

[2] G. Heinig, K. Rost, Split algorithms for centrosymmetric Toeplitz-plus-Hankel matrices with arbi-trary rank profile, in: Oper. Theory Adv. Appl., Birkhäuser, Basel, in press.

[3] G. Heinig, K. Rost, Schur-type algorithms for the solution of Hermitian Toeplitz systems via fac-torization, in: Oper. Theory Adv. Appl., vol. 160, Birkhäuser, Basel, 2005, pp. 233–252.

[4] G. Heinig, K. Rost, Fast “split” algorithms for Toeplitz and Toeplitz-plus-Hankel matrices witharbitrary rank profile, in: Proceedings of the International Conference on Mathematics and its Appli-cations (ICMA 2004), Kuwait, 2005, pp. 285–312.

[5] G. Heinig, K. Rost, Split algorithms for symmetric Toeplitz matrices with arbitrary rank profile,Numer. Linear Algebra Appl. 12 (2–3) (2005) 141–151.

[6] G. Heinig, K. Rost, Split algorithms for Hermitian Toeplitz matrices with arbitrary rank profile,Linear Algebra Appl. 392 (2004) 235–253.

[7] G. Heinig, Fast algorithms for Toeplitz least squares problems, Current trends in operator theoryand its applications, in: Oper. Theory Adv. Appl., vol. 149, Birkhäuser, Basel, 2004, pp. 167–197.

[8] G. Heinig, K. Rost, Split algorithms for skewsymmetric Toeplitz matrices with arbitrary rank profile,Theoret. Comput. Sci. 315 (2–3) (2004) 453–468.

[9] G. Heinig, K. Rost, New fast algorithms for Toeplitz-plus-Hankel matrices, SIAM J. Matrix Anal.Appl. 25 (3) (2003) 842–857.

[10] G. Heinig, K. Rost, Fast algorithms for centro-symmetric and centro-skewsymmetric Toeplitz-plus-Hankel matrices, in: International Conference on Numerical Algorithms, vol. I (Marrakesh, 2001),Numer. Algorithms 33 (1–4) (2003) 305–317.

K. Rost / Linear Algebra and its Applications 413 (2006) 1–12 7

[11] G. Heinig, Inversion of Toeplitz-plus-Hankel matrices with arbitrary rank profile, in: Fast Algorithmsfor Structured Matrices: Theory and Applications (South Hadley, MA, 2001), Contemp. Math., vol.323, Amer. Math. Soc., Providence, RI, 2003, pp. 75–89.

[11] M. Van Barel, G. Heinig, P. Kravanja, A superfast method for solving Toeplitz linear least squaresproblems, Special Issue on Structured Matrices: Analysis, Algorithms and Applications (Cortona,2000), Linear Algebra Appl. 366 (2003) 441–457.

[13] G. Heinig, K. Rost, Centrosymmetric and centro-skewsymmetric Toeplitz-plus-Hankel matrices andBezoutians, Special Issue on Structured Matrices: Analysis, Algorithms and Applications (Cortona,2000), Linear Algebra Appl. 366 (2003) 257–281.

[14] D. Bini, G. Heinig, E. Tyrtyshnikov (Eds.), Special Issue on Structured Matrices: Analysis, Algo-rithms and Applications, Papers from the workshop held in Cortona, September 21–28, 2000, LinearAlgebra Appl. 366 (2003).

[15] G. Heinig, K. Rost, Fast algorithms for skewsymmetric Toeplitz matrices, in: Toeplitz matricesand singular integral equations (Pobershau, 2001), Oper. Theory Adv. Appl., vol. 135, Birkhäuser,Basel, 2002, pp. 193–208.

[16] G. Heinig, On the reconstruction of Toeplitz matrix inverses from columns, Linear Algebra Appl.350 (2002) 199–212.

[17] G. Heinig, K. Rost, Centro-symmetric and centro-skewsymmetric Toeplitz matrices and Bezoutians,Special Issue on Structured and Infinite Systems of Linear Equations, Linear Algebra Appl. 343/344(2002) 195–209.

[18] G. Heinig, Kernel structure of Toeplitz-plus-Hankel matrices, Linear Algebra Appl. 340 (2002)1–13.

[19] G. Heinig, Fast and superfast algorithms for Hankel-like matrices related to orthogonal polynomials,in: Numerical Analysis and its Applications (Rousse, 2000), Lecture Notes in Comput. Sci., vol.1988, Springer, Berlin, 2001, pp. 385–392.

[20] M. Van Barel, G. Heinig, P. Kravanja, An algorithm based on orthogonal polynomial vectors forToeplitz least squares problems, in: Numerical Analysis and its Applications (Rousse, 2000), LectureNotes in Comput. Sci., vol. 1988, Springer, Berlin, 2001, pp. 27–34.

[21] M. Van Barel, G. Heinig, P. Kravanja, A stabilized superfast solver for nonsymmetric Toeplitzsystems, SIAM J. Matrix Anal. Appl. 23 (2) (2001) 494–510.

[22] G. Heinig, K. Rost, Efficient inversion formulas for Toeplitz-plus-Hankel matrices using trigonomet-ric transformations, in: Structured Matrices in Mathematics, Computer Science, and Engineering,vol. II (Boulder, CO, 1999), Contemp. Math., vol. 281, Amer. Math. Soc., Providence, RI, 2001,pp. 247–264.

[23] G. Heinig, Stability of Toeplitz matrix inversion formulas, in: Structured Matrices in Mathematics,Computer Science, and Engineering, vol. II (Boulder, CO, 1999), Contemp. Math., vol. 281, Amer.Math. Soc., Providence, RI, 2001, pp. 101–116.

[24] G. Heinig, V. Olshevsky, The Schur algorithm for matrices with Hessenberg displacement structure,in: Structured Matrices in Mathematics, Computer Science, and Engineering, vol. II (Boulder, CO,1999), Contemp. Math., vol. 281, Amer. Math. Soc., Providence, RI, 2001, 3–15.

[25] G. Heinig, Not every matrix is similar to a Toeplitz matrix, in: Proceedings of the Eighth Conferenceof the International Linear Algebra Society (Barcelona, 1999), Linear Algebra Appl. 332/334 (2001)519–531.

[26] G. Heinig, Chebyshev-Hankel matrices and the splitting approach for centro-symmetric Toeplitz-plus-Hankel matrices, Linear Algebra Appl. 327 (1–3) (2001) 181–196.

[27] S. Feldmann, G. Heinig, Partial realization for singular systems in standard form, Linear AlgebraAppl. 318 (1–3) (2000) 127–144.

[28] G. Heinig, K. Rost, Representations of inverses of real Toeplitz-plus-Hankel matrices using trigono-metric transformations, in: Large-scale Scientific Computations of Engineering and EnvironmentalProblems, vol. II (Sozopol, 1999), Notes Numer. Fluid Mech., vol. 73, Vieweg, Braunschweig, 2000,pp. 80–86.

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[29] M. Van Barel, G. Heinig, P. Kravanja, Least squares solution of Toeplitz systems based on orthogonalpolynomial vectors, in: F.T. Luk (Ed.), Advanced Signal Processing Algorithms, Architectures, andImplementations X, Proceedings of SPIE, vol. 4116, 2000, pp. 167–172.

[30] V. Maz’ya, S. Nazarov, B. Plamenevskij, Asymptotic theory of elliptic boundary value problems insingularly perturbed domains, vol. I (G. Heinig, C. Posthoff, Trans. from German), in: Oper. TheoryAdv. Appl., vol. 111, Birkhäuser, Basel, 2000.

[31] G. Heinig, K. Rost, Hartley transform representations of symmetric Toeplitz matrix inverses withapplication to fast matrix–vector multiplication, SIAM J. Matrix Anal. Appl. 22 (1) (2000) 86–105.

[32] G. Heinig, K. Rost, Hartley transform representations of inverses of real Toeplitz-plus-Hankel matri-ces, in: Proceedings of the International Conference on Fourier Analysis and Applications (Kuwait,1998), Numer. Funct. Anal. Optim. 21 (1–2) (2000) 175–189.

[33] F. Al-Musallam, A. Böttcher, P. Butzer, G. Heinig, Vu Kim Tuan (Eds.), in: Proceedings of theInternational Conference on Fourier Analysis and Applications, Held at Kuwait University, Kuwait,May 3–6, 1998, Numer. Funct. Anal. Optim. 21 (1–2) (2000).

[34] G. Heinig, F. Al-Musallam, Hermite’s formula for vector polynomial interpolation with applicationsto structured matrices, Appl. Anal. 70 (3–4) (1999) 331–345.

[35] S. Feldmann, G. Heinig, Parametrization of minimal rank block Hankel matrix extensions andminimal partial realizations, Integral Equations Operator Theory 33 (2) (1999) 153–171.

[36] G. Heinig, K. Rost, DFT representations of Toeplitz-plus-Hankel Bezoutians with application tofast matrix–vector multiplication, in: ILAS Symposium on Fast Algorithms for Control, Signals andImage Processing (Winnipeg, MB, 1997), Linear Algebra Appl. 284 (1–3) (1998) 157–175.

[37] G. Heinig, Matrices with higher order displacement structure, Linear Algebra Appl. 278 (1–3)(1998) 295–301.

[38] G. Heinig, A. Bojanczyk, Transformation techniques for Toeplitz and Toeplitz-plus-Hankel matrices.II: Algorithms, Linear Algebra Appl. 278 (1–3) (1998) 11–36.

[39] G. Heinig, Properties of “derived” Hankel matrices, in: Recent Progress in Operator Theory (Re-gensburg, 1995), Oper. Theory Adv. Appl., vol. 103, Birkhäuser, Basel, 1998, pp. 155–170.

[40] G. Heinig, K. Rost, Representations of Toeplitz-plus-Hankel matrices using trigonometric transfor-mations with application to fast matrix–vector multiplication, in: Proceedings of the Sixth Confer-ence of the International Linear Algebra Society (Chemnitz, 1996), Linear Algebra Appl. 275/276(1998) 225–248.

[41] G. Heinig, F. Al-Musallam, Lagrange’s formula for tangential interpolation with application tostructured matrices, Integral Equations Operator Theory 30 (1) (1998) 83–100.

[42] G. Heinig, Generalized Cauchy–Vandermonde matrices, Linear Algebra Appl. 270 (1998) 45–77.[43] G. Heinig, The group inverse of the transformation S(X) = 3DAX − XB, Linear Algebra Appl.

257 (1997) 321–342.[44] G. Heinig, A. Bojanczyk, Transformation techniques for Toeplitz and Toeplitz-plus-Hankel matrices.

I: Transformations, in: Proceedings of the Fifth Conference of the International Linear AlgebraSociety (Atlanta, GA, 1995), Linear Algebra Appl. 254 (1997) 193–226.

[45] G. Heinig, L.A. Sakhnovich, I.F. Tidniuk, Paired Cauchy matrices, Linear Algebra Appl. 251 (1997)189–214.

[46] G. Heinig, Solving Toeplitz systems after extension and transformation, in: Toeplitz Matrices:Structures, Algorithms and Applications (Cortona, 1996), Calcolo 33 (1–2) (1998) 115–129.

[47] S. Feldmann, G. Heinig, On the partial realization problem for singular systems, in: Proceedingsof the 27th Annual Iranian Mathematics Conference (Shiraz, 1996), Shiraz Univ., Shiraz, 1996, pp.79–100.

[48] S. Feldmann, G. Heinig, Vandermonde factorization and canonical representations of block Hankelmatrices, in: Proceedings of the Fourth Conference of the International Linear Algebra Society(ILAS) (Rotterdam, 1994), Linear Algebra Appl. 241/243 (1996) 247–278.

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[49] G. Heinig, Inversion of generalized Cauchy matrices and other classes of structured matrices, in:Linear Algebra for Signal Processing (Minneapolis, MN, 1992), IMA Vol. Math. Appl., vol. 69,Springer, New York, 1995, pp. 63–81.

[50] G. Heinig, Matrix representations of Bezoutians, Special Issue Honoring Miroslav Fiedler andVlastimil Pták, Linear Algebra Appl. 223/224 (1995) 337–354.

[51] G. Heinig, K. Rost, Recursive solution of Cauchy–Vandermonde systems of equations, LinearAlgebra Appl. 218 (1995) 59–72.

[52] G. Heinig, Generalized inverses of Hankel and Toeplitz mosaic matrices, Linear Algebra Appl. 216(1995) 43–59.

[53] G. Heinig, F. Hellinger, Displacement structure of generalized inverse matrices, in: GeneralizedInverses (1993), Linear Algebra Appl. 211 (1994) 67–83.

[54] G. Heinig, F. Hellinger, The finite section method for Moore–Penrose inversion of Toeplitz operators,Integral Equations Operator Theory 19 (4) (1994) 419–446.

[55] G. Heinig, F. Hellinger, Displacement structure of pseudoinverses, in: Second Conference of theInternational Linear Algebra Society (ILAS) (Lisbon, 1992), Linear Algebra Appl. 197/198 (1994)623–649.

[56] S. Feldmann, G. Heinig, Uniqueness properties of minimal partial realizations, Linear Algebra Appl.203/204 (1994) 401–427.

[57] G. Heinig, F. Hellinger, Moore–Penrose inversion of square Toeplitz matrices, SIAM J. Matrix Anal.Appl. 15 (2) (1994) 418–450.

[58] A.W. Bojanczyk, G. Heinig, A multi-step algorithm for Hankel matrices, J. Complexity 10 (1)(1994) 142–164.

[59] G. Heinig, F. Hellinger, On the Bezoutian structure of the Moore–Penrose inverses of Hankelmatrices, SIAM J. Matrix Anal. Appl. 14 (3) (1993) 629–645.

[60] T. Finck, G. Heinig, K. Rost, An inversion formula and fast algorithms for Cauchy–Vandermondematrices, Linear Algebra Appl. 183 (1993) 179–191.

[61] G. Heinig, P. Jankowski, Kernel structure of block Hankel and Toeplitz matrices and partial reali-zation, Linear Algebra Appl. 175 (1992) 1–30.

[62] G. Heinig, Inverse problems for Hankel and Toeplitz matrices, Linear Algebra Appl. 165 (1992)1–23.

[63] G. Heinig, Fast algorithms for structured matrices and interpolation problems, in: Algebraic Com-puting in Control (Paris, 1991), Lecture Notes in Control and Inform. Sci., vol. 165, Springer, Berlin,1991, pp. 200–211.

[64] G. Heinig, On structured matrices, generalized Bezoutians and generalized Christoffel–Darbouxformulas, in: Topics in Matrix and Operator Theory (Rotterdam, 1989), Oper. Theory Adv. Appl.,vol. 50, Birkhäuser, Basel, 1991, pp. 267–281.

[65] G. Heinig, Formulas and algorithms for block Hankel matrix inversion and partial realization, in:Signal Processing, Scattering and Operator Theory, and Numerical Methods (Amsterdam, 1989),Progr. Systems Control Theory, vol. 5, Birkhäuser Boston, Boston, MA, 1990, pp. 79–90.

[66] G. Heinig, P. Jankowski, Parallel and superfast algorithms for Hankel systems of equations, Numer.Math. 58 (1) (1990) 109–127.

[67] G. Heinig, P. Jankowski, Fast algorithms for the solution of general Toeplitz systems, Wiss. Z. Tech.Univ. Karl-Marx-Stadt 32 (1) (1990) 12–17.

[68] G. Heinig, K. Rost, Matrices with displacement structure, generalized Bezoutians, and Moebiustransformations, in: The Gohberg Anniversary Collection, vol. I (Calgary, AB, 1988), Oper. TheoryAdv. Appl., vol. 40, Birkhäuser, Basel, 1989, pp. 203–230.

[69] G. Heinig, K. Rost, Inversion of matrices with displacement structure, Integral Equations OperatorTheory 12 (6) (1989) 813–834.

[70] G. Heinig, W. Hoppe, K. Rost, Structured matrices in interpolation and approximation problems,Wiss. Z. Tech. Univ. Karl-Marx-Stadt 31 (2) (1989) 196–202.

10 K. Rost / Linear Algebra and its Applications 413 (2006) 1–12

[71] G. Heinig, K. Rost, Matrix representations of Toeplitz-plus-Hankel matrix inverses, Linear AlgebraAppl. 113 (1989) 65–78.

[72] G. Heinig, T. Amdeberhan, On the inverses of Hankel and Toeplitz mosaic matrices. SeminarAnalysis (Berlin, 1987/1988), Akademie-Verlag, Berlin, 1988, pp. 53–65.

[73] G. Heinig, P. Jankowski, K. Rost, Tikhonov regularisation for block Toeplitz matrices, Wiss. Z.Tech. Univ. Karl-Marx-Stadt 30 (1) (1988) 41–45.

[74] G. Heinig, K. Rost, On the inverses of Toeplitz-plus-Hankel matrices, Linear Algebra Appl. 106(1988) 39–52.

[75] G. Heinig, P. Jankowski, K. Rost, Fast inversion algorithms of Toeplitz-plus-Hankel matrices,Numer. Math. 52 (6) (1988) 665–682.

[76] G. Heinig, Structure theory and fast inversion of Hankel striped matrices. I, Integral EquationsOperator Theory 11 (2) (1988) 205–229.

[77] G. Heinig, K. Rost, Inversion of generalized Toeplitz-plus-Hankel matrices, Wiss. Z. Tech. Univ.Karl-Marx-Stadt 29 (2) (1987) 209–211.

[78] G. Heinig, U. Jungnickel, Hankel matrices generated by Markov parameters, Hankel matrix exten-sion, partial realization, and Padé-approximation, in: Operator Theory and Systems (Amsterdam,1985), Oper. Theory Adv. Appl., vol. 19, Birkhäuser, Basel, 1986, 231–253.

[79] G. Heinig, U. Jungnickel, Lyapunov equations for companion matrices, Linear Algebra Appl. 76(1986) 137–147.

[80] G. Heinig, U. Jungnickel, Hankel matrices generated by the Markov parameters of rational functions,Linear Algebra Appl. 76 (1986) 121–135.

[81] G. Heinig, Partial indices for Toeplitz-like operators, Integral Equations Operator Theory 8 (6)(1985) 805–824.

[82] G. Heinig, K. Rost, Fast inversion of Toeplitz-plus-Hankel matrices, Wiss. Z. Tech. Hochsch. Karl-Marx-Stadt 27 (1) (1985) 66–71.

[83] G. Heinig, U. Jungnickel, On the Bezoutian and root localization for polynomials, Wiss. Z. Tech.Hochsch. Karl-Marx-Stadt 27 (1) (1985) 62–65.

[84] G. Heinig, B. Silbermann, Factorization of matrix functions in algebras of bounded functions, in:Spectral Theory of Linear Operators and Related Topics (Timisoara/Herculane, 1983), Oper. TheoryAdv. Appl., vol. 14, Birkhäuser, Basel, 1984, pp. 157–177.

[85] G. Heinig, K. Rost, Algebraic methods for Toeplitz-like matrices and operators, in: Oper. TheoryAdv. Appl., vol. 13, Birkhäuser, Basel, 1984.

[86] G. Heinig, U. Jungnickel, On the Routh-Hurwitz and Schur-Cohn problems for matrix polynomialsand generalized Bezoutians, Math. Nachr. 116 (1984) 185–196.

[87] G. Heinig, K. Rost, Schnelle Invertierungsalgorithmen für einige Klassen von Matrizen (Fast inver-sion algorithms for some classes of matrices), Wiss. Z. Tech. Hochsch. Karl-Marx-Stadt 26 (2)(1984) 235–241 (in German).

[88] G. Heinig, K. Rost, Algebraic methods for Toeplitz-like matrices and operators, in: MathematicalResearch, vol. 19, Akademie-Verlag, Berlin, 1984.

[89] G. Heinig, K. Rost, Invertierung von Toeplitzmatrizen und ihren Verallgemeinerungen. I: Die Meth-ode der UV -Reduktion (Inversion of Toeplitz matrices and their generalizations. I: The method ofUV -reduction), Beiträge Numer. Math. 12 (1984) 55–73 (in German).

[90] G. Heinig, Generalized resultant operators and classification of linear operator pencils up to strongequivalence, in: Functions, Series, Operators, vols. I and II (Budapest, 1980), Colloq. Math. Soc.János Bolyai, vol. 35, North-Holland, Amsterdam, 1983, pp. 611–620.

[91] G. Heinig, Inversion of Toeplitz and Hankel matrices with singular sections, Wiss. Z. Tech. Hochsch.Karl-Marx-Stadt 25 (3) (1983) 326–333.

[92] G. Heinig, U. Jungnickel, Zur Lösung von Matrixgleichungen der Form AX − XB = 3DC (On thesolution of matrix equations of the form AX − XB = 3DC), Wiss. Z. Tech. Hochsch. Karl-Marx-Stadt 23 (4) (1981) 387–393 (German).

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[93] G. Heinig, Linearisierung und Realisierung holomorpher Operatorfunktionen, Wiss. Z. Tech. Ho-chsch. Karl-Marx-Stadt 22 (5) (1980) 453–459 (in German).

[94] G. Heinig, K. Rost, Invertierung einiger Klassen von Matrizen und Operatoren. I: Endliche Toeplitz-matrizen und ihre Verallgemeinerungen (Inversion of some classes of matrices and operators. I: FiniteToeplitz matrices and their generalizations), in: Wissenschaftliche Informationen (Scientific Infor-mation), vol. 12, Technische Hochschule Karl-Marx-Stadt, Sektion Mathematik, Karl-Marx-Stadt,1979 (in German).

[95] G. Heinig, Bezoutiante, Resultante und Spektralverteilungsprobleme für Operatorpolynome, Math.Nachr. 91 (1979) 23–43 (German).

[96] G. Heinig, Transformationen von Toeplitz- und Hankelmatrizen, Wiss. Z. Tech. Hochsch. Karl-Marx-Stadt 21 (7) (1979) 859–864 (in German).

[97] G. Heinig, Invertibility of singular integral operators, Soobshch. Akad. Nauk Gruzin. SSR 96 (1)(1979) 29–32 (in Russian).

[98] G. Heinig, Über ein kontinuierliches Analogon der Begleitmatrix eines Polynoms und die Linear-isierung einiger Klassen holomorpher Operatorfunktionen, Beiträge Anal. 13 (1979) 111–126 (inGerman).

[99] G. Heinig, Verallgemeinerte Resultantenbegriffe bei beliebigen Matrixbüscheln. II. Gemisch-ter Resultantenoperator, Wiss. Z. Tech. Hochsch. Karl-Marx-Stadt 20 (6) (1978) 701–703(in German).

[100] G. Heinig, Verallgemeinerte Resultantenbegriffe bei beliebigen Matrixbüscheln. I: Einseitiger Re-sultantenoperator, Wiss. Z. Tech. Hochsch. Karl-Marx-Stadt 20 (6) (1978) 693–700 (in German).

[101] G. Heinig, Endliche Toeplitzmatrizen und zweidimensionale Wiener–Hopf-Operatoren mit homog-enem Symbol. II: Über die normale Auflösbarkeit einer Klasse zweidimensionaler Wiener–HopfOperatoren, Math. Nachr. 82 (1978) 53–68 (in German).

[102] G. Heinig, Endliche Toeplitzmatrizen und zweidimensionale Wiener–Hopf-Operatoren mit homog-enem Symbol. I: Eigenschaften endlicher Toeplitzmatrizen, Math. Nachr. 82 (1978) 29–52.

[103] G. Heinig, K. Rost, Über homogene Gleichungen vom Faltungstyp auf einem endlichen Intervall,Demonstratio Math. 10 (3–4) (1977) 791–806 (in German).

[104] G. Heinig, Über Block-Hankelmatrizen und den Begriff der Resultante für Matrixpolynome, Wiss.Z. Techn. Hochsch. Karl-Marx-Stadt 19 (4) (1977) 513–519 (in German).

[105] G. Heinig, The notion of Bezoutian and of resultant for operator pencils, Funkcional. Anal. i Priložen.11 (3) (1977) 94–95 (in Russian).

[106] I.C. Gohberg, G. Heinig, The resultant matrix and its generalizations. II: The continual analogue ofthe resultant operator, Acta Math. Acad. Sci. Hungar. 28 (3–4) (1976) 189–209 (in Russian).

[107] G. Heinig, Periodische Jacobimatrizen im entarteten Fall, Wiss. Z. Techn. Hochsch. Karl-Marx-Stadt18 (4) (1976) 419–423 (in German).

[108] G. Heinig, Über die Invertierung und das Spektrum von singulären Integral-operatoren mit Ma-trixkoeffizienten, 5. Tagung über Probleme und Methoden der Mathematischen Physik (Techn.Hochschule Karl-Marx-Stadt, Karl-Marx-Stadt, 1975), Heft 1, Wiss. Schr. Techn. Hochsch. Karl-Marx-Stadt, Techn. Hochsch., Karl-Marx-Stadt, 1975, pp. 52–59 (in German).

[109] I.C. Gohberg, G. Heinig, On matrix integral operators on a finite interval with kernels depending onthe difference of the arguments, Rev. Roumaine Math. Pures Appl. 20 (1975) 55–73 (in Russian).

[110] I.C. Gohberg, G. Heinig, The resultant matrix and its generalizations. I: The resultant operator formatrix polynomials, Acta Sci. Math. (Szeged) 37 (1975) 41–61 (in Russian).

[111] I.C. Gohberg, G. Heinig, Inversion of finite Toeplitz matrices consisting of elements of a noncom-mutative algebra, Rev. Roumaine Math. Pures Appl. 19 (1974) 623–663 (in Russian).

[112] G. Heinig, The inversion and the spectrum of matrix Wiener–Hopf operators, Mat. Sb. (NS) 91(133) (1973) 253–266 (in Russian).

[113] G. Heinig, The inversion and the spectrum of matrix-valued singular integral operators, Mat. Issled.8 (3/29) (1973) 106–121 (in Russian).

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[114] I.C. Gohberg, G. Heinig, The inversion of finite Toeplitz matrices, Mat. Issled. 8 (3/29) (1973)151–156 (in Russian).

[115] G. Heinig, Inversion of periodic Jacobi matrices, Mat. Issled. 8 (1/27) (1973) 180–200 (in Russian).

Karla RostDepartment of Mathematics,

Chemnitz University of Technology,D-09107 Chemnitz, Germany

E-mail address: krost@mathematik.tu-chemnitz.de

Received 2 August 2005; accepted 30 August 2005Available online 26 October 2005