THE Effects of Rounding Error on an Algorithm for Downdating a Cholesky Factorization.

Abstract

Let the positive definite matrix A have a Cholesky factorization A = RtransposedR. For a given vector x suppose that A' = A - xxtransposed has a Cholesky factorization A' = R'transposedR'. This paper considers an algorithm for computing R' form R and x and an extension for removing a row from the QR factorization of a regression problem. It is shown that the algorithm is stable in the presence of rounding errors. However, it is also shown that the matrix R' can be a very ill-conditioned function of R and x. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1977
Accession Number
ADA045388

Entities

People

  • Gilbert W. Stewart

Organizations

  • University of Maryland

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Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Algorithms
  • Arithmetic
  • Computations
  • Computer Science
  • Eigenvalues
  • Error Analysis
  • Errors
  • Floating Point Operations
  • Mathematics
  • Military Research
  • New York
  • Perturbation Theory
  • Perturbations
  • Precision
  • Rotation
  • Square Roots
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Fields of Study

  • Mathematics

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  • Linear Algebra