Crout Algorithm with Accumulated Inner Product

Abstract

A posteriori forward error analysis is applied to the Crout algorithm with inner product accumulation in solving system of linear algebraic equations of the type Ax = b. By attributing the generated round-off errors properly to the matrices A and b, it is shown, under certain reasonable assumptions, that the computed x satisfies a new perturbed system such that (A + delta A)x = b + delta b and the upper bounds for delta A and delta b in infinite norm are shown to be proportional to n, the system order. This is an improvement over the results where the inner products are not accumulated.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1972
Accession Number
AD0741775

Entities

People

  • Nai-kuan Tsao

Organizations

  • Air Force Research Laboratory

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  • Materials and Manufacturing Processes
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  • Air Force
  • Algorithms
  • Applied Mathematics
  • Arithmetic
  • Arithmetic Units
  • Classification
  • Computations
  • Decomposition
  • Department Of Defense
  • Equations
  • Error Analysis
  • Errors
  • Floating Point Operations
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  • United States

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  • Approximation Theory.
  • Systems Analysis and Design