000 05331cam a2200361Ia 4500
003 OCoLC
005 20241128141028.0
008 070802s1996 enka ob 001 0 eng d
020 _a9780125535601
020 _a0125535600
020 _a9780080519128
020 _a0080519121
041 _aEnglish
049 _aMAIN
072 7 _aMAT
_x003000
_2bisacsh
082 0 4 _a519.4
_222
_bPHI
100 1 _aPhillips, G. M.
100 1 _q(George McArtney)
245 1 0 _aTheory and applications of numerical analysis /
_cG.M. Phillips and P.J. Taylor.
250 _a2nd ed.
260 _aLondon ;
_aSan Diego :
_bAcademic Press,
_c1996.
300 _a1 online resource (xii, 447 pages) :
_billustrations.
504 _aIncludes bibliographical references (pages 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 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.
506 _aAccess restricted to subscribing institutions.
520 _aThis 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.
650 0 _aNumerical analysis.
700 1 _aTaylor, Peter John.
856 4 0 _uhttps://ezproxy.lib.gla.ac.uk/login?url=https://www.sciencedirect.com/science/book/9780125535601
856 4 0 _zConnect to e-book
907 _a.b38152174
942 _2ddc
_cBOOKS
999 _c43871
_d43871