Deflated Lanczos Procedures for Solving Nearly Singular Systems.

Abstract

This document considers the solution of the linear sytem Ax = b, where A is nearly singular. The solution x can be uniquely decomposed into two parts: a generally large component in the direction of the approximate null space of A, and a part that is orthogonal to it. In many applications, it is desirable to compute this deflated decomposition in a stable and efficient manner. This apper proposes an iterative algorithm based on the Lanczos process, for the case where A is symmetric. The method requires access to A only in the form of a matrix-vector product Av and is efficient for large problems. No a priori knowledge of the approximate null space is needed. Keywords: Orthogonality; Convergence; Matrices(Mathematics); and Numerical analysis. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1985
Accession Number
ADA161971

Entities

People

  • Tony F. Chan
  • Youcef Saad

Organizations

  • Yale University

Tags

Communities of Interest

  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Chebyshev Polynomials
  • Computations
  • Convergence
  • Decomposition
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Errors
  • Inequalities
  • Intervals
  • Iterations
  • Linear Systems
  • Nonlinear Systems
  • Orthogonality
  • Polynomials
  • Precision

Fields of Study

  • Mathematics

Readers

  • Applied Combinatorial Optimization and Logic Circuit Design.
  • Approximation Theory.
  • Graph Algorithms and Convex Optimization.

Technology Areas

  • Space