A New Derivation of Symmetric Positive Definite Secant Updates.

Abstract

In this paper, we introduce a simple new set of techiques for deriving symmetric and positive definite secant updates. We use these techniques to present a simple new derivation of the BFGS update using neither matrix inverses nor weighting matrices. A related derivation is shown to generate a large class of symmetric rank-two update formulas, together with the condition for each to preserve positive definiteness. We apply our techniques to generate a new projected BFGS update, and indicate applications to the efficient implementation of secant algorithms via the Cholsky factorization. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1980
Accession Number
ADA093060

Entities

People

  • J. E. Dennis Jr.
  • Robert B. Schnabel

Organizations

  • University of Colorado Boulder

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  • Algebra
  • Algorithms
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  • Mathematics

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  • Linear Algebra
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