General Algorithm Based Error Correction and Orthogonal Polynomials,

Abstract

We explore the relationships between sequences of orthogonal polynomials and the process of error correction based on the use of weighted checksums, often called Algorithm Based Fault Tolerance. We show that the latter process can be reduced to a problem in orthogonal polynomials. We then use methods for generating sequences of orthogonal polynomials to solve the error correction problem, where the checksums are computed using rather general sets of weights. The methods are equivalent to the matrix Lanczos tridiagonalization process. We give a simple numerical example.

Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1992
Accession Number
ADP006601

Entities

People

  • Daniel Boley

Organizations

  • University of Minnesota

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Fault Tolerance
  • Mathematics
  • Polynomials
  • Sequences

Fields of Study

  • Mathematics

Readers

  • Computer Programming and Software Development.
  • Linear Algebra