ISBN-10:
0387904557
ISBN-13:
9780387904559
Pub. Date:
03/18/1980
Publisher:
Springer New York
Conjugate Direction Methods in Optimization / Edition 1

Conjugate Direction Methods in Optimization / Edition 1

by M.R. Hestenes

Hardcover

Current price is , Original price is $199.0. You
Select a Purchase Option (1980)
  • purchase options
    $134.16 $199.00 Save 33% Current price is $134.16, Original price is $199. You Save 33%.
  • purchase options

Product Details

ISBN-13: 9780387904559
Publisher: Springer New York
Publication date: 03/18/1980
Series: Stochastic Modelling and Applied Probability , #12
Edition description: 1980
Pages: 325
Product dimensions: 6.10(w) x 9.25(h) x 0.24(d)

Table of Contents

I Newton’s Method and the Gradient Method.- 1 Introduction.- 2 Fundamental Concepts.- 3 Iterative Methods for Solving g(x) = 0.- 4 Convergence Theorems.- 5 Minimization of Functions by Newton’s Method.- 6 Gradient Methods—The Quadratic Case.- 7 General Descent Methods.- 8 Iterative Methods for Solving Linear Equations.- 9 Constrained Minima.- II Conjugate Direction Methods.- 1 Introduction.- 2 Quadratic Functions on En.- 3 Basic Properties of Quadratic Functions.- 4 Minimization of a Quadratic Function F on k-Planes.- 5 Method of Conjugate Directions (CD-Method).- 6 Method of Conjugate Gradients (CG-Algorithm).- 7 Gradient PARTAN.- 8 CG-Algorithms for Nonquadratic Functions.- 9 Numerical Examples.- 10 Least Square Solutions.- III Conjugate Gram-Schmidt Processes.- 1 Introduction.- 2 A Conjugate Gram-Schmidt Process.- 3 CGS-CG-Algorithms.- 4 A Connection of CGS-Algorithms with Gaussian Elimination.- 5 Method of Parallel Displacements.- 6 Methods of Parallel Planes (PARP).- 7 Modifications of Parallel Displacements Algorithms.- 8 CGS-Algorithms for Nonquadratic Functions.- 9 CGS-CG-Routines for Nonquadratic Functions.- 10 Gauss-Seidel CGS-Routines.- 11 The Case of Nonnegative Components.- 12 General Linear Inequality Constraints.- IV Conjugate Gradient Algorithms.- 1 Introduction.- 2 Conjugate Gradient Algorithms.- 3 The Normalized CG-Algorithm.- 4 Termination.- 5 Clustered Eigenvalues.- 6 Nonnegative Hessians.- 7 A Planar CG-Algorithm.- 8 Justification of the Planar CG-Algorithm.- 9 Modifications of the CG-Algorithm.- 10 Two Examples.- 11 Connections between Generalized CG-Algorithms and Stadard CG- and CD-Algorithm.- 12 Least Square Solutions.- 13 Variable Metric Algorithms.- 14 A Planar CG-Algorithm for Nonquadratic Functions.- References.

Customer Reviews

Most Helpful Customer Reviews

See All Customer Reviews