Some Inverse Problems for Jacobi and Arrow Matrices

Abstract

We consider the problem of reconstructing Jacobi matrices and real symmetric arrow matrices from two eigenpairs. Algorithms for solving these inverse problems are presented. We show that there are reasonable conditions under which this reconstruction is always possible. Moreover, it is seen that in certain cases reconstruction can proceed with little or no cancellation. The algorithm is particularly elegant for the tridiagonal matrix associated with a bidiagonal singular value decomposition.... Jacobi matrix, Arrow matrix, Inverse problems.

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Document Details

Document Type
Technical Report
Publication Date
Oct 13, 1992
Accession Number
ADA262336

Entities

People

  • Carlos Borgeds
  • Ruggero Frezza
  • William B. Gragg

Organizations

  • Naval Postgraduate School

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Cancellation
  • Classification
  • Computations
  • Decomposition
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Interlacing
  • Inverse Problems
  • Mathematics
  • Military Research
  • Orthogonality
  • Security
  • Three Dimensional

Fields of Study

  • Mathematics

Readers

  • Linear Algebra