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Author Phillips, G. M. (George McArtney)

Title Theory and applications of numerical analysis / G.M. Phillips and P.J. Taylor.

Imprint London ; San Diego : Academic Press, 1996.

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Location Call No. OPAC Message Status
 Axe Elsevier ScienceDirect Ebook  Electronic Book    ---  Available
Edition 2nd ed.
Description 1 online resource (xii, 447 pages) : illustrations
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
text file rdaft http://rdaregistry.info/termList/fileType/1002.
Summary This text is a self-contained Second Edition, providing an introductory account of the main topics in numerical analysis. The book emphasizes both the theorems which show the underlying rigorous mathematics and the algorithms which define precisely how to program the numerical methods. Both theoretical and practical examples are included. * a unique blend of theory and applications * two brand new chapters on eigenvalues and splines * inclusion of formal algorithms * numerous fully worked examples * a large number of problems, many with solutions.
Contents (Chapter Heading): Introduction. Basic Analysis. Taylors Polynomial and Series. The Interpolating Polynomial. Best Approximation. Splines and Other Approximations. Numerical Integration and Differentiation. Solution of Algebraic Equations of One Variable. Linear Equations. Matrix Norms and Applications. Matrix Eigenvalues and Eigenvectors. Systems of Non-linear Equations. Ordinary Differential Equations. Boundary Value and Other Methods for Ordinary Differential Equations. Appendices. Solutions to Selected Problems. References. Subject Index. -- Introduction: What is Numerical Analysis? Numerical Algorithms. Properly Posed and Well-Conditioned Problems. Basic Analysis: Functions. Limits and Derivatives. Sequences and Series. Integration. Logarithmic and Exponential Functions. Taylor's Polynomial and Series: Function Approximation. Taylor's Theorem. Convergence of Taylor Series. Taylor Series in Two Variables. Power Series. The Interpolating Polyomial: Linear Interpolation. Polynomial Interpolation. Accuracy of Interpolation. The Neville-Aitken Algorithm. Inverse Interpolation. Divided Differences. Equally Spaced Points. Derivatives and Differences. Effect of Rounding Error. Choice of Interpolation Points. Examples of Bernstein and Runge. "Best"Approximation: Norms of Functions. Best Approximations. Least Squares Approximations. Orthogonal Functions. Orthogonal Polynomials. Minimax Approximation. Chebyshev Series. Economization of Power Series. The Remez Algorithms. Further Results on Minimax Approximation. Splines and Other Approximations: Introduction. B-Splines. Equally-Spaced Knots. Hermite Interpolation. Pade and Rational Approximation. Numerical Integration and Differentiation: Numerical Integration. Romberg Integration. Gaussian Integration. Indefinite Integrals. Improper Integrals. Multiple Integrals. Numerical Differentiation. Effect of Errors. Solution of Algebraic Equations of One Variable: Introduction. The Bisection Method. Interpolation Methods. One-Point Iterative Methods. Faster Convergence. Higher Order Processes. The Contraction Mapping Theorem. Linear Equations: Introduction. Matrices. Linear Equations. Pivoting. Analysis of Elimination Method. Matrix Factorization. Compact Elimination Methods. Symmetric Matrices. Tridiagonal Matrices. Rounding Errors in Solving Linear Equations. Matrix Norms and Applications: Determinants, Eigenvalues, and Eigenvectors. Vector Norms. Matrix Norms. Conditioning. Iterative Correction from Residual Vectors. Iterative Methods. Matrix Eigenvalues and Eigenvectors: Relations Between Matrix Norms and Eigenvalues; Gerschgorin Theorems. Simple and Inverse Iterative Method. Sturm Sequence Method. The QR Algorithm. Reduction to Tridiagonal Form: Householder's Method. Systems of Non-Linear Equations: Contraction Mapping Theorem. Newton's Method. Ordinary Differential Equations: Introduction. Difference Equations and Inequalities. One-Step Methods. Truncation Errors of One-Step Methods. Convergence of One-Step Methods. Effect of Rounding Errors on One-Step Methods. Methods Based on Numerical Integration; Explicit Methods. Methods Based on Numerical Integration; Implicit Methods. Iterating with the Corrector. Milne's Method of Estimating Truncation Errors. Numerical Stability. Systems and Higher Order Equations. Comparison of Step-by-Step Methods. Boundary Value and Other Methods for Ordinary Differential Equations: Shooting Method for Boundary Value Problems. Boundary Value Problem. Extrapolation to the Limit. Deferred Correction. Chebyshev Series Method. Appendices. Solutions to Selected Problems. References. Subject Index.
Bibliography Includes bibliographical references (pages 440-441) and index.
Note Print version record.
Subject Numerical analysis.
Analyse numérique.
MATHEMATICS -- Applied.
Numerical analysis
ANÁLISE NUMÉRICA.
Genre/Form dissertations.
Academic theses
Academic theses.
Thèses et écrits académiques.
Added Author Taylor, Peter John.
Other Form: Print version: Phillips, G.M. (George McArtney). Theory and applications of numerical analysis. 2nd ed. London ; San Diego : Academic Press, 1996 0125535600 9780125535601 (OCoLC)35455584
ISBN 9780125535601
0125535600
9780080519128 (electronic bk.)
0080519121 (electronic bk.)
Standard No. (WaSeSS)ssj0000258073
AU@ 000048130452
CHNEW 001005260
DEBBG BV036962214
DEBBG BV039830083
DEBBG BV042317234
DEBBG BV043044921
DEBSZ 275751414
DEBSZ 422177032
NZ1 12434028
NZ1 14540430

 
    
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