Research in Efficient Scientific Computation

Abstract

The more common obstacle, called curable breakdown, is handled by LookAhead versions of the algorithm. This term was introduced earlier by Prof. Parlett and is now the generally accepted way to implement the Lanczos algorithm. Now that the algorithm is understood theoretically good implementations are being developed in many groups. Another long quest that Prof. Parlett completed in this period was to understand the phenomenon of Forward Instability in the symmetric tridiagonal QR algorithm. We now know when and only when this alarming phenomenon can occur. It is invariable associated with premature deflation of an eigenvalue. Through a series of delays the paper was not published until January 1993. In a completely different view Prof. Parlett, and a gifted student Wu-Liang Heng, developed a novel approach to the 2D Ising model problem that arises in Statistical Mechanics. The new method enable us to solve cases close to criticality for n = 30, and even up to 35. Other methods cannot get beyond n = 18 for reasonable costs. This work is only available in technical reports at present. The following lists show that a lot of other commendable work was either published or completed during this period.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1992
Accession Number
ADA262084

Entities

People

  • Beresford N. Parlett

Organizations

  • University of California, Berkeley

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Applied Mathematics
  • Computations
  • Contracts
  • Eigenvalues
  • Engineering
  • Linear Algebra
  • Mathematical Analysis
  • Mathematics
  • Numerical Analysis
  • Parallel Computing
  • Programming Languages
  • Signal Processing
  • Statistical Mechanics
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  • Two Dimensional

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  • Theoretical Analysis.