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

Contents:

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.