A Direct Decomposition Method for the Solution of Sparse Linear Least Squares Problems

Abstract

Given a sparse nonsquare system of linear equations Mx = b where M(T) M is either dense or full, we present a direct method that generates a least squares solution of the original system by solving a smaller least squares problem. The method accomplishes this decomposition by applying orthogonal transformations to a restructured form of the original system of equations Mx = b. The algorithms derived from the decomposition result are well suited for both sequential and parallel architecture machines. In a specific Navy signal processing application, the presented algorithm computed on a Sun SPARC 10 workstation a least squares solution of a rank deficient system comprising 703 equations and 592 variables in a number of floating point computations tenfold smaller than a method that does not exploit the sparsity structure of M. Sparse linear least squares

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1994
Accession Number
ADA284060

Entities

People

  • A. K. Kevorkian

Organizations

  • Naval Command, Control and Ocean Surveillance Center

Tags

Communities of Interest

  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algebra
  • Algorithms
  • Buildings And Structures
  • Computations
  • Elimination
  • Equations
  • Floating Point Operations
  • Least Squares Method
  • Linear Algebra
  • Military Research
  • Ocean Surveillance
  • Parallel Computing
  • Scattering
  • Signal Processing
  • Sparse Matrix
  • Test And Evaluation
  • Trees (Data Structures)

Fields of Study

  • Engineering

Readers

  • Linear Algebra
  • Parallel and Distributed Computing.