A New Method of Solving Ill-Conditioned Systems of Equations.

Abstract

The problems associated with ill-conditioned matrices are well known and widespread. As of yet, there are no general solutions to the problem. The only remedies are usually ad hoc and are extremely case-dependent. This paper presents a method which gives good results for a large variety of situations. The method involves masking, a technique which sets the lower-order bits (the number of bits varies) to zero, and then applying standard system-of-equations solvers. Most of the computer runs made used the Hilbert matrix, and either a specified b vector (as in the form, Ax = b), or a specified x vector, with the b obtained by multiplying x by A. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1981
Accession Number
ADA115569

Entities

People

  • Brian S. Birmingham

Organizations

  • Air Force Institute of Technology

Tags

Communities of Interest

  • Cyber
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Classification
  • Computations
  • Computer Programming
  • Computers
  • Convergence
  • Engineering
  • Equations
  • Errors
  • Iterations
  • Mathematical Analysis
  • Numbers
  • Rational Numbers
  • Real Numbers
  • Residuals
  • Security
  • Standards

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Operations Research
  • Systems Analysis and Design