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Theory and applications of numerical...

Phillips, G. M.

Theory and applications of numerical analysis

Record Type:	Electronic resources : Monograph/item
Title/Author:	Theory and applications of numerical analysisG.M. Phillips and P.J. Taylor.
Author:	Phillips, G. M.
other author:	Taylor, Peter John.
Published:	London ;Academic Press,1996.
Description:	xii, 447 p. :ill. ;23 cm.
Subject:	Numerical analysis.
Online resource:	An electronic book accessible through the World Wide Web; click for information
Online resource:	http://www.engineeringvillage.com/controller/servlet/OpenURL?genre=book&isbn=9780125535601
ISBN:	9780125535601

Theory and applications of numerical analysis
Phillips, G. M.

Theory and applications of numerical analysis[electronic resource] /G.M. Phillips and P.J. Taylor. - 2nd ed. - London ;Academic Press,1996. - xii, 447 p. :ill. ;23 cm.

Includes bibliographical references (p. [440]-441) and index.

(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 ofNon-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.

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.

Electronic reproduction.
Amsterdam :
Elsevier Science & Technology,
2007.

Mode of access: World Wide Web.

ISBN: 9780125535601

Source: 81730:81730Elsevier Science & Technologyhttp://www.sciencedirect.comSubjects--Topical Terms:

182073
Numerical analysis.
Index Terms--Genre/Form:

214472
Electronic books.

LC Class. No.: QA297 / .P52 1996eb

Dewey Class. No.: 519.4

Theory and applications of numerical analysis
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035 $a ocn162129115
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082 0 4 $a 519.4 $2 22
100 1 $a Phillips, G. M. $q (George McArtney) $3 452284
245 1 0 $a Theory and applications of numerical analysis $h [electronic resource] / $c G.M. Phillips and P.J. Taylor.
250 $a 2nd ed.
260 $a London ; $a San Diego : $b Academic Press, $c 1996.
300 $a xii, 447 p. : $b ill. ; $c 23 cm.
504 $a Includes bibliographical references (p. [440]-441) and index.
505 0 $a (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 ofNon-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.
520 $a 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.
533 $a Electronic reproduction. $b Amsterdam : $c Elsevier Science & Technology, $d 2007. $n Mode of access: World Wide Web. $n System requirements: Web browser. $n Title from title screen (viewed on July 25, 2007). $n Access may be restricted to users at subscribing institutions.
650 0 $a Numerical analysis. $3 182073
650 7 $a AN�ALISE NUM�ERICA $2 larpcal $3 455288
655 7 $a Electronic books. $2 local. $3 214472
700 1 $a Taylor, Peter John. $3 455287
710 2 $a ScienceDirect (Online service) $3 307425
776 1 $c Original $z 0125535600 $z 9780125535601 $w (OCoLC)35455584
856 4 0 $3 ScienceDirect $u http://www.sciencedirect.com/science/book/9780125535601 $z An electronic book accessible through the World Wide Web; click for information
856 4 0 $3 Referex $u http://www.engineeringvillage.com/controller/servlet/OpenURL?genre=book&isbn=9780125535601 $z An electronic book accessible through the World Wide Web; click for information
994 $a C0 $b TEF