Some New Methods for Solving Linear Equations.

Abstract

It takes of the order of N-cubed operations to solve a set of N linear equations in N unknowns. When the underlying physical problem has some time- or shift-invariance properties, the coefficient matrix is of Toeplitz (or difference or convolution) type and the equations can be with O(N-squared) operations. We have shown that with any nonsingular N x N matrix, we can associate an integer alpha between 1 and N such that it takes O(N-squared alpha operations to invert the matrix. The number alpha may be small for many non-Toeplitz matrices of physical interest. Some aspects of this result are discussed here, including extensions to continuous time kernels and integral equations. (Author)

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1976
Accession Number
ADA050976

Entities

People

  • Thomas Kailath

Organizations

  • Stanford University

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Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Applied Mathematics
  • Covariance
  • Data Science
  • Differential Equations
  • Displacement
  • Electrical Engineering
  • Equations
  • Information Science
  • Integral Equations
  • Integrals
  • Mathematics
  • New York
  • Scientific Research
  • Statistical Analysis
  • Statistics

Fields of Study

  • Mathematics

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  • Linear Algebra