An Clase-01 Algoritmo y Aproximacion Numerica Mar05ago2014 Sem2015-i
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Transcript of An Clase-01 Algoritmo y Aproximacion Numerica Mar05ago2014 Sem2015-i
Facultad de Ingenieriacutea UNAM Anaacutelisis Numeacuterico (Semestre 2015-I) Clase 01 (Martes 06 de agosto del 2014)
Paacutegina 1 de 4 Dr Rogelio Hernaacutendez
Introduccioacuten histoacuterica de los meacutetodos numeacutericos
Ejemplo 1 La tabla Babilonia
Numerical analysis is the study of algorithms for the problems of continuous mathematics (as distinguished
from discrete mathematics)
One of the earliest mathematical writing is the Babylonian tablet YBC 7289 which gives a sexagesimal
numerical approximation of the length of the diagonal in a unit square[1] Being able to compute the sides
of a triangle (and hence being able to compute square roots) is extremely important for instance in carpentry
and construction[2] In a square wall section that is two meters by two meters a diagonal beam has to be
meters long[3]
Numerical analysis continues this long tradition of practical mathematical calculations Much like the
Babylonian approximation to modern numerical analysis does not seek exact answers because exact
answers are impossible to obtain in practice Instead much of numerical analysis is concerned with obtaining
approximate solutions while maintaining reasonable bounds on errors
Numerical analysis naturally finds applications in all fields of engineering and the physical sciences but in the
21st century the life sciences and even the arts have adopted elements of scientific computations Ordinary
differential equations appear in the movement of heavenly bodies (planets stars and galaxies) optimization
occurs in portfolio management numerical linear algebra is essential to quantitative psychology stochastic
differential equations and Markov chains are essential in simulating living cells for medicine and
biologyBefore the advent of modern computers numerical methods often depended on hand interpolation in
large printed tables Nowadays (after mid 20th century) these tables have fallen into disuse because computers
can calculate the required functions The interpolation algorithms nevertheless may be used as part of the
software for solving differential equations and the like
Facultad de Ingenieriacutea UNAM Anaacutelisis Numeacuterico (Semestre 2015-I) Clase 01 (Martes 06 de agosto del 2014)
Paacutegina 2 de 4 Dr Rogelio Hernaacutendez
Ejemplo 2) El algoritmo numeacuterico para calcular la raiacutez ldquom-eacutesimardquo de un nuacutemero ldquoardquo es
Y para las raiacuteces cuadrada cuacutebica cuarta y quinta correspondientes son
Raiacutez Algoritmo numeacuterico
Cuadrada
Cuacutebica
Cuarta
Quinta
Facultad de Ingenieriacutea UNAM Anaacutelisis Numeacuterico (Semestre 2015-I) Clase 01 (Martes 06 de agosto del 2014)
Paacutegina 3 de 4 Dr Rogelio Hernaacutendez
Aproximacioacuten numeacuterica
Ejemplo) Determine radic120783120785120791120782120787
Presente las aproximaciones numeacutericas en forma tabular y graacutefica
Solucioacuten
El algoritmo numeacuterico correspondiente es
Considerando 1199090 = 15 se obtiene
Comportamiento estable y convergente
Facultad de Ingenieriacutea UNAM Anaacutelisis Numeacuterico (Semestre 2015-I) Clase 01 (Martes 06 de agosto del 2014)
Paacutegina 4 de 4 Dr Rogelio Hernaacutendez
Comportamiento inestable y convergente
Facultad de Ingenieriacutea UNAM Anaacutelisis Numeacuterico (Semestre 2015-I) Clase 01 (Martes 06 de agosto del 2014)
Paacutegina 2 de 4 Dr Rogelio Hernaacutendez
Ejemplo 2) El algoritmo numeacuterico para calcular la raiacutez ldquom-eacutesimardquo de un nuacutemero ldquoardquo es
Y para las raiacuteces cuadrada cuacutebica cuarta y quinta correspondientes son
Raiacutez Algoritmo numeacuterico
Cuadrada
Cuacutebica
Cuarta
Quinta
Facultad de Ingenieriacutea UNAM Anaacutelisis Numeacuterico (Semestre 2015-I) Clase 01 (Martes 06 de agosto del 2014)
Paacutegina 3 de 4 Dr Rogelio Hernaacutendez
Aproximacioacuten numeacuterica
Ejemplo) Determine radic120783120785120791120782120787
Presente las aproximaciones numeacutericas en forma tabular y graacutefica
Solucioacuten
El algoritmo numeacuterico correspondiente es
Considerando 1199090 = 15 se obtiene
Comportamiento estable y convergente
Facultad de Ingenieriacutea UNAM Anaacutelisis Numeacuterico (Semestre 2015-I) Clase 01 (Martes 06 de agosto del 2014)
Paacutegina 4 de 4 Dr Rogelio Hernaacutendez
Comportamiento inestable y convergente
Facultad de Ingenieriacutea UNAM Anaacutelisis Numeacuterico (Semestre 2015-I) Clase 01 (Martes 06 de agosto del 2014)
Paacutegina 3 de 4 Dr Rogelio Hernaacutendez
Aproximacioacuten numeacuterica
Ejemplo) Determine radic120783120785120791120782120787
Presente las aproximaciones numeacutericas en forma tabular y graacutefica
Solucioacuten
El algoritmo numeacuterico correspondiente es
Considerando 1199090 = 15 se obtiene
Comportamiento estable y convergente
Facultad de Ingenieriacutea UNAM Anaacutelisis Numeacuterico (Semestre 2015-I) Clase 01 (Martes 06 de agosto del 2014)
Paacutegina 4 de 4 Dr Rogelio Hernaacutendez
Comportamiento inestable y convergente