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Introduction to precise numerical methods /
Precise numerical analysis may be defined as the study of computer methods for solving mathematical problems either exactly or to prescribed accuracy. This book explains how precise numerical analysis is constructed. The book also provides exercises which illustrate points from the text and referenc...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Amsterdam ; Boston :
Academic Press,
©2007.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Acknowledgments; 1 Introduction; 1.1 Open-source software; 1.2 Calling up a program; 1.3 Log files and print files; 1.4 More on log files; 1.5 The tilde notation for printed answers; 2 Computer Arithmetics; 2.1 Floating-point arithmetic; 2.2 Variable precision floating-point arithmetic; 2.3 Interval arithmetic; 2.4 Range arithmetic; 2.5 Practical range arithmetic; 2.6 Interval arithmetic notation; 2.7 Computing standard functions in range arithmetic; 2.8 Rational arithmetic; Software Exercises A; Notes and References; 3 Classification of Numerical Computation Problems; 3.1 A knotty problem
- 3.2 The impossibility of untying the knot 3.3 Repercussions from nonsolvable problem 3.1; 3.4 Some solvable and nonsolvable decimal place problems; 3.5 The solvable problems handled by calc; 3.6 Another nonsolvable problem; 3.7 The trouble with discontinuous functions; Notes and References; 4 Real-Valued Functions; 4.1 Elementary functions; Software Exercises B; 5 Computing Derivatives; 5.1 Power series of elementary functions; 5.2 An example of series evaluation; 5.3 Power series for elementary functions of several variables; 5.4 A more general method of generating power series
- 5.5 The demo program derivSoftware Exercises C; Notes and References; 6 Computing Integrals; 6.1 Computing a definite integral; 6.2 Formal interval arithmetic; 6.3 The demo program integ for computing ordinary definite integrals; 6.4 Taylor's remainder formula generalized; 6.5 The demo program mulint for higher dimensional integrals; 6.6 The demo program imprint for computing improper integrals; Software Exercises D; Notes and References; 7 Finding Where a Function f(x) is Zero; 7.1 Obtaining a solvable problem; 7.2 Using interval arithmetic for the problem; 7.3 Newton's method
- 7.4 Order of convergence Software Exercises E; 8 Finding Roots of Polynomials; 8.1 Polynomials; 8.2 A bound for the roots of a polynomial; 8.3 The Bairstow method for finding roots of a real polynomial; 8.4 Bounding the error of a rational polynomial's root approximations; 8.5 Finding accurate roots for a rational or a real polynomial; 8.6 The demo program roots; Software Exercises F; Notes and References; 9 Solving n Linear Equations in n Unknowns; 9.1 Notation; 9.2 Computation problems; 9.3 A method for solving linear equations; 9.4 Computing determinants
- 9.5 Finding the inverse of a square matrix 9.6 The demo programs equat, r_equat, and c_equat; Software Exercises G; Notes and References; 10 Eigenvalue and Eigenvector Problems; 10.1 Finding a solution to Ax= 0 when det A= 0; 10.2 Eigenvalues and Eigenvector; 10.3 Companion matrices and Vandermonde matrices; 10.4 Finding eigenvalues and Eigenvector by Danilevsky's method; 10.5 Error bounds for Danilevsky's method; 10.6 Rational matrices; 10.7 The demo programs eigen, c_eigen, and r_eigen; Software Exercises H; 11 Problems of Linear Programming; 11.1 Linear algebra using rational arithmetic