Numerical analysis / L. Ridgway Scott.

Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for comp...

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Bibliographic Details
Main Author: Scott, L. Ridgway
Language:English
Published: Princeton, N.J. : Princeton University Press, [2011], ©2011.
Subjects:
Numerical analysis.
Physical Description:xiv, 325 pages : illustrations ; 24 cm
Format: Book

MARC

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100 1 |a Scott, L. Ridgway.  |0 http://id.loc.gov/authorities/names/n93103565 
245 1 0 |a Numerical analysis /  |c L. Ridgway Scott. 
260 |a Princeton, N.J. :  |b Princeton University Press,  |c [2011], ©2011. 
300 |a xiv, 325 pages :  |b illustrations ;  |c 24 cm 
336 |a text  |b txt  |2 rdacontent 
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504 |a Includes bibliographical references (pages [311]-322) and index. 
505 0 |a Machine generated contents note: ch. 1 Numerical Algorithms -- 1.1.Finding roots -- 1.2.Analyzing Heron's algorithm -- 1.3.Where to start -- 1.4.An unstable algorithm -- 1.5.General roots: effects of floating-point -- 1.6.Exercises -- 1.7.Solutions -- ch. 2 Nonlinear Equations -- 2.1.Fixed-point iteration -- 2.2.Particular methods -- 2.3.Complex roots -- 2.4.Error propagation -- 2.5.More reading -- 2.6.Exercises -- 2.7.Solutions -- ch. 3 Linear Systems -- 3.1.Gaussian elimination -- 3.2.Factorization -- 3.3.Triangular matrices -- 3.4.Pivoting -- 3.5.More reading -- 3.6.Exercises -- 3.7.Solutions -- ch. 4 Direct Solvers -- 4.1.Direct factorization -- 4.2.Caution about factorization -- 4.3.Banded matrices -- 4.4.More reading -- 4.5.Exercises -- 4.6.Solutions -- ch. 5 Vector Spaces -- 5.1.Normed vector spaces -- 5.2.Proving the triangle inequality -- 5.3.Relations between norms -- 5.4.Inner-product spaces -- 5.5.More reading -- 5.6.Exercises -- 5.7.Solutions -- ch. 6 Operators -- 6.1.Operators -- 6.2.Schur decomposition -- 6.3.Convergent matrices -- 6.4.Powers of matrices -- 6.5.Exercises -- 6.6.Solutions -- ch. 7 Nonlinear Systems -- 7.1.Functional iteration for systems -- 7.2.Newton's method -- 7.3.Limiting behavior of Newton's method -- 7.4.Mixing solvers -- 7.5.More reading -- 7.6.Exercises -- 7.7.Solutions -- ch. 8 Iterative Methods -- 8.1.Stationary iterative methods -- 8.2.General splittings -- 8.3.Necessary conditions for convergence -- 8.4.More reading -- 8.5.Exercises -- 8.6.Solutions -- ch. 9 Conjugate Gradients -- 9.1.Minimization methods -- 9.2.Conjugate Gradient iteration -- 9.3.Optimal approximation of CG -- 9.4.Comparing iterative solvers -- 9.5.More reading -- 9.6.Exercises -- 9.7.Solutions -- ch. 10 Polynomial Interpolation -- 10.1.Local approximation: Taylor's theorem -- 10.2.Distributed approximation: interpolation -- 10.3.Norms in infinite-dimensional spaces -- 10.4.More reading -- 10.5.Exercises -- 10.6.Solutions -- ch. 11 Chebyshev and Hermite Interpolation -- 11.1.Error term -- 11.2.Chebyshev basis functions -- 11.3.Lebesgue function -- 11.4.Generalized interpolation -- 11.5.More reading -- 11.6.Exercises -- 11.7.Solutions -- ch. 12 Approximation Theory -- 12.1.Best approximation by polynomials -- 12.2.Weierstrass and Bernstein -- 12.3.Least squares -- 12.4.Piecewise polynomial approximation -- 12.5.Adaptive approximation -- 12.6.More reading -- 12.7.Exercises -- 12.8.Solutions -- ch. 13 Numerical Quadrature -- 13.1.Interpolatory quadrature -- 13.2.Peano kernel theorem -- 13.3.Gregorie-Euler-Maclaurin formulas -- 13.4.Other quadrature rules -- 13.5.More reading -- 13.6.Exercises -- 13.7.Solutions -- ch. 14 Eigenvalue Problems -- 14.1.Eigenvalue examples -- 14.2.Gershgorin's theorem -- 14.3.Solving separately -- 14.4.How not to eigen -- 14.5.Reduction to Hessenberg form -- 14.6.More reading -- 11.7.Exercises -- 14.8.Solutions -- ch. 15 Eigenvalue Algorithms -- 15.1.Power method -- 15.2.Inverse iteration -- 15.3.Singular value decomposition -- 15.4.Comparing factorizations -- 15.5.More reading -- 15.6.Exercises -- 15.7.Solutions -- ch. 16 Ordinary Differential Equations -- 16.1.Basic theory of ODEs -- 16.2.Existence and uniqueness of solutions -- 16.3.Basic discretization methods -- 16.4.Convergence of discretization methods -- 16.5.More reading -- 16.6.Exercises -- 16.7.Solutions -- ch. 17 Higher-order ODE Discretization Methods -- 17.1.Higher-order discretization -- 17.2.Convergence conditions -- 17.3.Backward differentiation formulas -- 17.4.More reading -- 17.5.Exercises -- 17.6.Solutions -- ch. 18 Floating Point -- 18.1.Floating-point arithmetic -- 18.2.Errors in solving systems -- 18.3.More reading -- 18.4.Exercises -- 18.5.Solutions -- ch. 19 Notation. 
520 |a Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for computing expressions defined with real numbers. Emphasizing the theory behind the computation, this book provides a rigorous and self-contained introduction to numerical analysis and presents the advanced mathematics that underpin industrial software, including complete details that are missing from most textbooks. 
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