嶺東科技大學 |

Numerical analysis

紀錄類型:	書目-語言資料,印刷品 : 單行本
作者:	ScottL. Ridgway,
出版地:	Princeton, N.J.
出版者:	Princeton University Press;
出版年:	c2011
面頁冊數:	xiv, 325 p.ill. : 24 cm.;
標題:	Numerical analysis. -
ISBN:	978-0-691-14686-7bound
ISBN:	0-691-14686-1bound
內容註:	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

Numerical analysis
Scott, L. Ridgway

Numerical analysis / L. Ridgway Scott - Princeton, N.J. : Princeton University Press, c2011. - xiv, 325 p. ; ill. ; 24 cm..
Machine generated contents note: ch. 1 Numerical Algorithms.
Includes bibliographical references (p. [311]-322) and index..
ISBN 978-0-691-14686-7ISBN 0-691-14686-1
Numerical analysis.

Numerical analysis
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327 1 $a Machine generated contents note: ch. 1 Numerical Algorithms $a 1.1.Finding roots $a 1.2.Analyzing Heron's algorithm $a 1.3.Where to start $a 1.4.An unstable algorithm $a 1.5.General roots: effects of floating-point $a 1.6.Exercises $a 1.7.Solutions $a ch. 2 Nonlinear Equations $a 2.1.Fixed-point iteration $a 2.2.Particular methods $a 2.3.Complex roots $a 2.4.Error propagation $a 2.5.More reading $a 2.6.Exercises $a 2.7.Solutions $a ch. 3 Linear Systems $a 3.1.Gaussian elimination $a 3.2.Factorization $a 3.3.Triangular matrices $a 3.4.Pivoting $a 3.5.More reading $a 3.6.Exercises $a 3.7.Solutions $a ch. 4 Direct Solvers $a 4.1.Direct factorization $a 4.2.Caution about factorization $a 4.3.Banded matrices $a 4.4.More reading $a 4.5.Exercises $a 4.6.Solutions $a ch. 5 Vector Spaces $a 5.1.Normed vector spaces $a 5.2.Proving the triangle inequality $a 5.3.Relations between norms $a 5.4.Inner-product spaces $a 5.5.More reading $a 5.6.Exercises $a 5.7.Solutions $a ch. 6 Operators $a 6.1.Operators $a 6.2.Schur decomposition $a 6.3.Convergent matrices $a 6.4.Powers of matrices $a 6.5.Exercises $a 6.6.Solutions $a ch. 7 Nonlinear Systems $a 7.1.Functional iteration for systems $a 7.2.Newton's method $a 7.3.Limiting behavior of Newton's method $a 7.4.Mixing solvers $a 7.5.More reading $a 7.6.Exercises $a 7.7.Solutions $a ch. 8 Iterative Methods $a 8.1.Stationary iterative methods $a 8.2.General splittings $a 8.3.Necessary conditions for convergence $a 8.4.More reading $a 8.5.Exercises $a 8.6.Solutions $a ch. 9 Conjugate Gradients $a 9.1.Minimization methods $a 9.2.Conjugate Gradient iteration $a 9.3.Optimal approximation of CG $a 9.4.Comparing iterative solvers $a 9.5.More reading $a 9.6.Exercises $a 9.7.Solutions $a ch. 10 Polynomial Interpolation $a 10.1.Local approximation: Taylor's theorem $a 10.2.Distributed approximation: interpolation $a 10.3.Norms in infinite-dimensional spaces $a 10.4.More reading $a 10.5.Exercises $a 10.6.Solutions $a ch. 11 Chebyshev and Hermite Interpolation $a 11.1.Error term $a 11.2.Chebyshev basis functions $a 11.3.Lebesgue function $a 11.4.Generalized interpolation $a 11.5.More reading $a 11.6.Exercises $a 11.7.Solutions $a ch. 12 Approximation Theory $a 12.1.Best approximation by polynomials $a 12.2.Weierstrass and Bernstein $a 12.3.Least squares $a 12.4.Piecewise polynomial approximation $a 12.5.Adaptive approximation $a 12.6.More reading $a 12.7.Exercises $a 12.8.Solutions $a ch. 13 Numerical Quadrature $a 13.1.Interpolatory quadrature $a 13.2.Peano kernel theorem $a 13.3.Gregorie-Euler-Maclaurin formulas $a 13.4.Other quadrature rules $a 13.5.More reading $a 13.6.Exercises $a 13.7.Solutions $a ch. 14 Eigenvalue Problems $a 14.1.Eigenvalue examples $a 14.2.Gershgorin's theorem $a 14.3.Solving separately $a 14.4.How not to eigen $a 14.5.Reduction to Hessenberg form $a 14.6.More reading $a 11.7.Exercises $a 14.8.Solutions $a ch. 15 Eigenvalue Algorithms $a 15.1.Power method $a 15.2.Inverse iteration $a 15.3.Singular value decomposition $a 15.4.Comparing factorizations $a 15.5.More reading $a 15.6.Exercises $a 15.7.Solutions $a ch. 16 Ordinary Differential Equations $a 16.1.Basic theory of ODEs $a 16.2.Existence and uniqueness of solutions $a 16.3.Basic discretization methods $a 16.4.Convergence of discretization methods $a 16.5.More reading $a 16.6.Exercises $a 16.7.Solutions $a ch. 17 Higher-order ODE Discretization Methods $a 17.1.Higher-order discretization $a 17.2.Convergence conditions $a 17.3.Backward differentiation formulas $a 17.4.More reading $a 17.5.Exercises $a 17.6.Solutions $a ch. 18 Floating Point $a 18.1.Floating-point arithmetic $a 18.2.Errors in solving systems $a 18.3.More reading $a 18.4.Exercises $a 18.5.Solutions $a ch. 19 Notation
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