Conference: Three Decades of Numerical Linear Algebra at Berkeley

Abstract

We study the problem of minimizing the norm, the norm of the inverse and the condition number with respect to the spectral norm, when a submatrix of a matrix can be chosen arbitrarily. For the norm minimization problem we give a different proof than that given by Davis/Kahan/Weinberger. This new approach can then also be used to characterize the completions that minimize the norm of the inverse. For the problem of optimizing the condition number we give a partial result. Condition number, Norm of a matrix, Matrix completion, Dilation theory, Robust regularization of descriptor systems.

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Document Details

Document Type
Technical Report
Publication Date
Apr 30, 1993
Accession Number
ADA264964

Entities

People

  • James Demmel

Organizations

  • University of California, Berkeley

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algebra
  • Algorithms
  • Applied Mathematics
  • Arithmetic
  • California
  • Computer Science
  • Computers
  • Electronic Mail
  • Engineering
  • Equations
  • Inverse Problems
  • Linear Algebra
  • Mathematics
  • Numerical Analysis
  • Optimization
  • Perturbations
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Computational Modeling and Simulation
  • Linear Algebra