Numerical Analysis

ISBN-10: 0691146861
ISBN-13: 9780691146867
Edition: 2011
Authors: L. Ridgway Scott
List price: $70.95
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Book details

List price: $70.95
Copyright year: 2011
Publisher: Princeton University Press
Publication date: 5/8/2011
Binding: Hardcover
Pages: 344
Size: 6.25" wide x 9.25" long x 1.00" tall
Weight: 1.342
Language: English

Preface
Numerical Algorithms
Finding roots
Analyzing Heron's algorithm
Where to start
An unstable algorithm
General roots: effects of floating-point
Exercises
Solutions
Nonlinear Equations
Fixed-point iteration
Particular methods
Complex roots
Error propagation
More reading
Exercises
Solutions
Linear Systems
Gaussian elimination
Factorization
Triangular matrices
Pivoting
More reading
Exercises
Solutions
Direct Solvers
Direct factorization
Caution about factorization
Banded matrices
More reading
Exercises
Solutions
Vector Spaces
Normed vector spaces
Proving the triangle inequality
Relations between norms
Inner-product spaces
More reading
Exercises
Solutions
Operators
Operators
Schur decomposition
Convergent matrices
Powers of matrices
Exercises
Solutions
Nonlinear Systems
Functional iteration for systems
Newton's method
Limiting behavior of Newton's method
Mixing solvers
More reading
Exercises
Solutions
Iterative Methods
Stationary iterative methods
General splittings
Necessary conditions for convergence
More reading
Exercises
Solutions
Conjugate Gradients
Minimization methods
Conjugate Gradient iteration
Optimal approximation of CG
Comparing iterative solvers
More reading
Exercises
Solutions
Polynomial Interpolation
Local approximation: Taylor's theorem
Distributed approximation: interpolation
Norms in infinite dimensional spaces
More reading
Exercises
Solutions
Chebyshev and Hermite Interpolation
Error term �
Chebyshev basis functions
Lebesgue function
Generalized interpolation
More reading
Exercises
Solutions
Approximation Theory
Best approximation by polynomials
Weierstrass and Bernstein
Least squares
Piecewise polynomial approximation
Adaptive approximation
More reading
Exercises
Solutions
Numerical Quadrature
Interpolatory quadrature
Peano kernel theorem
Gregorie Euler Maclaurin formulas
Other quadrature rules
More reading
Exercises
Solutions
Eigenvalue Problems
Eigenvalue examples
Gershgorin's theorem
Solving separately
How not to eigen
Reduction to Hessenberg form
More reading
Exercises
Solutions
Eigenvalue Algorithm
Power method
Inverse iteration
Singular value decomposition
Comparing factorizations
More reading
Exercises
Solutions
Ordinary Differential Equations
Basic theory of ODEs
Existence and uniqueness of solutions
Basic discretization methods
Convergence of discretization methods
More reading
Exercises
Solutions
Higher-order ODE Discretization Methods
Higher-order discretization
Convergence conditions
Backward differentiation formulas
More reading
Exercises
Solutions
Floating Point
Floating-point arithmetic
Errors in solving systems
More reading
Exercises
Solutions
Notation
Bibliography
Index

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