References

[1] Anderssen, R.S., de Hoog, F.R., and Lukas, M.A. The Applicationand Numerical Solution of Integral Equations. Sijthoff and Noordhoff,Alphen aan den Rijn 1980.

[2] Anselone, P.M. Collectively Compact Operator Approximation The­ory and Applications to Integral Equations. Prentice-Hall, EnglewoodCliffs 1971.

[3] Atkinson, K.E. A Survey of Numerical Methods for the Solution ofFredholm Integral Equations of the Second Kind. SIAM, Philadelphia1976.

[4] Aubin, J.P. Approximation of Elliptic Boundary Value Problems.John Wiley & Sons, New York 1972.

[5] Aubin, J.P. Applied Functional Analysis. John Wiley & Sons, NewYork 1979.

[6] Baker, C.T.H. The Numerical Treatment of Integral Equations.Clarendon Press, Oxford 1977.

[7] Ben-Israel, A. and Greville, T.N.E. Generalized Inverses: Theory andApplications. John Wiley & Sons, New York 1974.

[8] Brandt, A. Multigrid adaptive solutions to boundary value problems,Math. Compo 31, 333-390 (1977).

318 References

[9] Brass, H. Quadraturverfahren. Vandenhoek und Ruprecht, Gottingen1979.

[10] Brosowski, B. and Kress, R. Einfiihrung in die Numerische Mathe­matik. Bibliographisches Institut, Mannheim 1975.

[11] Ciarlet, P.S. The Finite Element Method for Elliptic Problems. NorthHolland, Amsterdam 1978.

[12] Coddington, E.A. and Levinson, N. Theory of Ordinary DifferentialEquations. McGraw-Hill, New York 1955.

[13] Collatz, L. The Numerical Treatment of Differential Equations. 3rdedition. Springer-Verlag, Berlin 1966.

[14] Colton, D. and Kress, R. Inverse Acoustic and Electromagnetic Scat­tering Theory. 2nd edition. Springer-Verlag, Berlin 1998.

[15] Davis, P.J. On the numerical integration of periodic analytic func­tions. In: Symposium on Numerical Approximation (R. Langer, ed.).The University of Wisconsin Press, Madison, 45-59 (1959).

[16] Davis, P.J. Interpolation and Approximation. Blaisdell PublishingCompany, Waltham 1963.

[17] Davis, P.J. and Rabinowitz, P. Methods of Numerical Integration. 2ndedition. Academic Press, San Diego 1984.

[18] De Boor, C. A Practical Guide to Splines. Springer-Verlag, New York1978.

[19] Delves, L.M. and Mohamed, J.L. Computational Methods for IntegralEquations. Cambridge University Press, Cambridge 1985.

[20] Dennis, J.E. and Schnabel, R.B. Numerical Methods for Uncon­strained Optimization and Nonlinear Equations. Prentice-Hall, En­glewood Cliffs 1983.

[21] Engels, H. Numerical Quadrature and Cubature. Academic Press,New York 1980.

[22] Engl, H.W., Hanke, M., and Neubauer, A. Regularization of InverseProblems. Kluwer Academic Publishers, Dordrecht 1996.

[23] Farin, G. Curves and Surfaces for Computer Aided Geometric Design.A Practical Guide. 2nd edition. Academic Press, Boston 1990.

[24] Gilbarg, D. and Trudinger, N.S. Elliptic Partial Differential Equa­tions of Second Order. Springer-Verlag, Berlin 1977.

References 319

[25] Golberg, M.A. and Chen, C.S. Discrete Projection Methods for Inte­gral Equations. Computational Mechanics Publications, Southamp­ton 1997.

[26] Golub, G. and Ortega, J.M. Scientific Computing. Academic Press,Boston 1993.

[27] Golub, G. and van Loan, C. Matrix Computations. John HopkinsUniversity Press, Baltimore 1989.

[28] Groetsch, C.W. The Theory of Tikhonov Regularization for FredholmEquations of the First Kind. Pitman, Boston 1984.

[29] Hackbusch, W. Multi-Grid Methods and Applications. Springer­Verlag, Berlin 1985.

[30] Hackbusch, W. Integral Equations: Theory and Numerical Treatment.Birkhauser-Verlag, Basel 1995.

[31] Hadamard, J. Lectures on Cauchy's Problem in Linear Partial Dif­ferential Equations. Yale University Press, New Haven 1923.

[32] Hairer, E., N0rsett, S.P., and Wanner, G. Solving Ordinary Differen­tial Equations. Nonstiff Problems. Springer-Verlag, Berlin 1987.

[33] Henrici, P. Discrete Variable Methods in Ordinary Differential Equa­tions. John Wiley & Sons, New York 1962.

[34] Heuser, H. Funktionalanalysis. 2. Auflage. Teubner, Stuttgart 1986.

[35] Kantorovic, L.V. and Akilov, G.P. Functional Analysis in NormedSpaces. Pergamon Press, Oxford 1964.

[36] Keller, H.B. Numerical Methods for Two-Point Boundary ValueProblems. Blaisdell Publishing Company, Waltham 1968.

[37] Kirsch, A. An Introduction to the Mathematical Theory of InverseProblems. Springer-Verlag, New York 1996.

[38] Kress, REin ableitungsfreies Restglied fur die trigonometrische In­terpolation periodischer analytischer Funktionen. Numer. Math. 16,389-396 (1971).

[39] Kress, R Linear Integral Equations. Springer-Verlag, Berlin 1989.

[40] Kress, R A Nystrom method for boundary integral equations in do­mains with corners. Numer. Math. 58, 145-161 (1990).

[41] Kress, R, de Vries, H.L., and Wegmann, R On nonnormal matrices.Linear Algebra and its Appl. 8, 109-120 (1974).

320 References

[42] Lambert, J.D. Numerical Methods for Ordinary Differential Equa­tions. The Initial Value Problem. John Wiley & Sons, Chichester1993.

[43] Louis, A.K. Inverse und schlecht gestellte Probleme. Teubner, Stutt­gart 1989.

[44] More, J.J. The Levenberg-Marquardt algorithm, implementation andtheory. In: Numerical Analysis (Watson, ed.). Springer-Verlag Lec­ture Notes in Mathematics 630, Berlin, 105-116 (1977).

[45] Nussbaumer, H.J. Fast Fourier Transform and Convolution Algo­rithms. Springer-Verlag, Berlin 1982.

[46] Ortega, J.M. and Poole, W.G. An Introduction to Numerical Methodsfor Differential Equations. Pitman, Boston 1981.

[47] Ortega, J.M. and Rheinboldt, W.C. Iterative Solution of NonlinearEquations in Several Variables. Academic Press, New York 1970.

[48] Parlett, B.N. The Symmetric Eigenvalue Problem. Prentice-Hall, En­glewood Cliffs 1980.

[49] Prossdorf, S. and Silbermann, B. Numerical Analysis for Integraland Related Operator Equations. Akademie-Verlag, Berlin 1991, andBirkhauser-Verlag, Basel 1991.

[50] Roberts, S.M. and Shipman, J.S. Two-Point Boundary Value Prob­lems: Shooting Methods. Elsevier, New York 1972.

[51] Rudin, W. Functional Analysis. McGraw-Hill, New York 1973.

[52] Sag, T.W. and Szegeres, G. Numerical evaluation of high-dimensionalintegrals. Math. Compo 18, 245-253 (1964).

[53] Schumaker, L.L. Spline Functions: Basic Theory. John Wiley & Sons,Chichester 1981.

[54] Sidi, A. A new variable transformation for numerical integration. In:Numerical Integration IV. (Brass, Hammerlin, eds.) InternationalSeries of Numerical Mathematics. Birkhauser-Verlag Basel 112, 359­373 (1993).

[55] Stetter, H.J. Analysis of Discretization Methods for Ordinary Differ­ential Equations. Springer-Verlag, Berlin 1973.

[56] Stetter, H. J. The defect correction principle and discretization meth­ods, Numer. Math. 29, 425-443 (1978).

References 321

[57] Stroud, A.H. Approximate Calculation of Multiple Integrals. Prentice­Hall, Englewood Cliffs 1971.

[58] Takahasi, H. and Mori, M. Quadrature formulas obtained by variabletransformation. Numer. Math. 21, 206-219 (1973).

[59] Taylor, A.E. Introduction to Functional Analysis. John Wiley & Sons,New York 1967.

[60] Treves, F. Basic Linear Partial Differential Equations. AcademicPress, New York 1975.

[61] Varga, R. Matrix Iterative Analysis. Prentice-Hall, Englewood Cliffs1962.

[62] Watkins, D.S. Understanding the QR-Algorithm, SIAM Review 24,(1982).

[63] Weissinger, J. Spiirlich besetzte Gleichungssysteme. BibliographischesInstitut, Mannheim 1990.

[64] Wesseling, P. An Introduction to Multigrid Methods. John Wiley &Sons, Chichester 1992.

[65] Wilkinson, J .H. The Algebraic Eigenvalue Problem. Clarendon Press,Oxford 1965.

[66] Young, D. Iterative Solution of Large Linear Systems. AcademicPress, New York 1971.

Index

Adams-Bashforth method, 244Adams-Moulton method, 245adjoint matrix, 6Aitken's (P method, 117algebraic multiplicity, 36a posteriori estimate, 45a priori estimate, 44Aubin-Nitsche lemma, 282

backward substitution, 12, 15Bairstow method, 113Banach space, 40Banach's fixed point theorem, 43Banach-Steinhaus theorem, 314Bernoulli polynomial, 207Bernstein polynomial, 180best approximation, 47Bezier curve, 181Bezier points, 181Bezier polygon, 181Bezier spline, 183bijective operator, 46boundary value problem, 258

weak solution, 277bounded operator, 33bounded set, 29B-spline, 173

Cauchy sequence, 40

Cauchy-Schwarz inequality, 30Cea's lemma, 273characteristic polynomial, 36, 249Chebyshev polynomial, 204, 223Chebyshev quadrature, 223Cholesky elimination, 19classical Jacobi method, 131closed ball, 29closed set, 28closure, 28collectively compact operators, 294collocation method, 302collocation points, 302compact operator, 288complete pivoting, 15complete set, 40computer-aided geometric design,

179condition number, 80conjugate gradient method, 285consistency, 235, 245, 246

order, 235, 245, 246consistently ordered matrix, 64continuous operator, 32contraction number, 43contraction operator, 43convergence order, 108, 238convergent quadrature, 198

convergent sequence, 27convex hull, 181convex set, 98cyclic Jacobi method, 132

de Casteljau algorithm, 183defect correction iteration, 69defect correction principle, 69dense set, 28diagonal matrix, 16diagonalizable matrix, 133diagonally dominant, 56

strictly, 56weakly, 59

difference equation, 248stable, 248

direct methods, 5, 119discrepancy principle, 85distance, 27divergent sequence, 27divided differences, 154

eigenvalue, 36eigenvector, 36elimination methods, 5equicontinuous, 289equivalent linear system, 12equivalent norm, 27Euclidean norm, 26Euler method, 231

implicit, 233improved,234

Euler-Maclaurin expansion, 209explicit method, 233extrapolation method, 212, 216

fast Fourier transform, 167Fibonacci numbers, 256finite difference method, 262finite element method, 279fixed point, 43forward differences, 182forward elimination, 13, 14Fourier series, 52Fourier transform

Index 323

discrete, 167fast, 167

Fredholm integral equation, 287first kind, 287, 312second kind, 287

Friedrich inequality, 282Frobenius norm, 127frozen Newton method, 109fully discrete method, 274function space

era, b], 40Hi [a, b], 275L2 [a, b], 42

Galerkin method, 272Gauss-Chebyshev quadrature, 205Gauss-Jordan elimination, 18Gauss-Legendre quadrature, 205Gauss-Lobatto quadrature, 223Gauss-Radau quadrature, 223Gauss-Seidel method, 57

with relaxation, 62Gaussian elimination, 11, 14Gaussian quadrature, 201

composite, 207geometric multiplicity, 36global convergence, 95global error, 238

maximal, 238Gram-Schmidt orthogonalization,

31

Hermite interpolation operator, 161Hermite interpolation polynomial,

160Hermite-Birkhoff interpolation poly-

nomial, 186Hermitian matrix, 37Hessenberg matrix, 144Hessian matrix, 114Heun method, 234Hilbert matrix, 79Hilbert space, 40Horner scheme, 110Householder matrix, 20

324 Index

ill-conditioned linear system, 81ill-posed problem, 77implicit method, 233initial value problem, 228injective operator, 46inner product, 29interpolation operator, 157, 302

trigonometric, 169interpolation polynomial

Hermite, 160Hermite-Birkhoff, 186Lagrange, 153Newton, 155trigonometric, 163

interpolatory quadrature, 190inverse interpolation, 186irreducible matrix, 59iterative methods, 5, 119

Jacobi method, 55classical, 131cyclic, 132damped,71with relaxation, 61

Jacobian matrix, 99

kernel, 287degenerate, 315weakly singular, 291

Lagrange factor, 153Lagrange interpolation polynomial,

153least squares method, 10left triangular matrix, 18Legendre polynomial, 205Levenberg-Marquardt method, 114limit, 27linear convergence, 108linear interpolation, 158linear operator, 32linear system

equivalent, 12triangular, 12

Lipschitz condition, 228

Lipschitz constant, 228Lipschitz continuous, 43local convergence, 95local discretization error, 235, 245Lotka-Volterra equations, 255lower triangular matrix, 18LR decomposition, 18L 1 norm, 41L 2 norm, 42

Mandelbrot set, 118matrix

adjoint, 6consistently ordered, 64diagonal, 16diagonalizable, 133Hermitian, 37Hessenberg, 144Hessian, 114Hilbert, 79Householder, 20irreducible, 59Jacobian, 99left triangular, 18lower triangular, 18normal, 127permutation, 19positive definite, 19, 37positive semidefinite, 37reducible, 59right triangular, 18symmetric, 19transposed, 6tridiagonal, 7unitary, 20upper triangular, 18Vandermonde, 186

matrix norm, 34maximum norm, 26, 41mean value theorem, 99midpoint rule, 206Milne-Thomson method, 245modified Newton method, 109Moore-Penrose inverse, 84multigrid methods, 74

multiplicityalgebraic, 36geometric, 36

multistep method, 243stable, 251

Neumann series, 46, 51Neville scheme, 156Newton interpolation polynomial,

155Newton method, 102

frozen, 109modified, 109

Newton-Cotes quadrature, 191,222norm, 26

equivalent, 27Euclidean, 26Frobenius, 127£1,41£2,42maximum, 26, 41stronger, 50vector, 26

normal equations, 49normal matrix, 127normed space, 26Nystrom method, 245, 296

open ball, 29open set, 28operator, 32

bijective, 46bounded,33compact, 288continuous, 32contraction, 43injective, 46linear, 32strictly coercive, 269surjective, 46

operator norm, 33ordinary differential equation, 226orthogonal, 31orthogonal projection, 48orthogonal system, 31

Index 325

orthonormal system, 31

Parseval equality, 52partial pivoting, 15Peano kernel, 221permutation matrix, 19pivot element, 14pivoting

complete, 15partial, 15

polygon method, 231polynomial

Bernoulli, 207Bernstein, 180Chebyshev, 204, 223Legendre, 205

positive definite matrix, 19, 37positive semidefinite matrix, 37power method, 133predictor corrector method, 234pre-Hilbert space, 29projection method, 272, 303pseudo-inverse, 84

QR algorithm, 133deflation, 144shift, 144

QR decomposition, 19quadratic convergence, 108quadrature

Chebyshev, 223convergent, 198Gauss-Chebyshev, 205Gauss-Legendre, 205Gauss-Lobatto, 223Gauss-Radau, 223Gaussian, 201interpolatory, 190Newton-Cotes, 191, 222Romberg, 213

quadrature points, 190quadrature weights, 190

range, 32rank one methods, 110

326 Index

Rayleigh-Ritz method, 285rectangular rule, 210reducible matrix, 59regularization parameter, 86relaxation methods, 60relaxation parameter, 61Riesz theory, 289right triangular matrix, 18Romberg quadrature, 213root condition, 249Runge-Kutta method, 241

Sassenfeld criterion, 57scalar product, 29scaling, 16Schur's inequality, 127secant method, 110semidiscrete method, 274series, 50sesquilinear function, 270

bounded, 270strictly coercive, 270

shooting method, 258multiple, 261

Simpson's rule, 192composite, 196

simultaneous displacements, 55single-step method, 234singular system, 82singular value decomposition, 82singular values, 81Sobolev space, 275span, 31spectral cutoff, 85spectral radius, 38spline, 169

cubic, 170, 175spline interpolation, 169steepest descent, 115Steffensen's method, 117strictly coercive operator, 269stronger norm, 50Sturm-Liouville problem, 274successive approximations, 44successive displacements, 57

successive overrelaxation method,62

superlinear convergence, 110surjective operator, 46symmetric matrix, 19

theoremArzela-Ascoli, 289Courant, 123Faber, 160Gerschgorin, 126Kahan, 62Lax-Milgram, 269Marcinkiewicz, 159Ostrowski, 63Picard-Lindel6f, 228Rayleigh, 122Riesz, 268Steklow, 199Szego, 198Young, 64

Tikhonov regularization, 86transposed matrix, 6trapezoidal rule, 192

composite, 196triangle inequality, 26

second,26triangular linear system, 12tridiagonal matrix, 7trigonometric interpolation poly-

nomial, 163trigonometric polynomial, 162two-grid methods, 68

uniform boundedness principle, 292unitary matrix, 20upper triangular matrix, 18

Vandermonde matrix, 186vector norm, 26Verhulst equation, 227Volterra integral equation, 228, 314

weak derivative, 275well-conditioned linear system, 81well-posed problem, 77

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