NUMERICAL TECHNIQUES IN MATHEMATICAL PROGRAMMING

Abstract

The application of numerically stable matrix decompositions to minimization problems involving linear constraints is discussed and shown to be feasible without undue loss of efficiency. Part A describes computation and updating of the product-form of the LU decomposition of a matrix and shows it can be applied to solving linear systems at least as efficiently as standard techniques using the product-form of the inverse. Part B discusses orthogonalization via Householder transformations, with applications to least squares and quadratic programming algorithms based on the principal pivoting method of Cottle and Dantzig. Part C applies the singular value decomposition to the nonlinear least squares problem and discusses related eigenvalue problems.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1970
Accession Number
AD0709564

Entities

People

  • G. H. Golub
  • Mark A. Saunders
  • R. H. Bartels

Organizations

  • Stanford University

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Arithmetic
  • Computational Science
  • Computations
  • Computer Programming
  • Computer Science
  • Eigenvalues
  • Equations
  • Evolutionary Algorithms
  • Linear Programming
  • Mathematical Programming
  • Notation
  • Optimization
  • Quadratic Programming
  • Simplex Method
  • Systems Engineering

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Operations Research