A Note on an Inverse Eigenproblem for Band Matrices

Abstract

An efficient rotation pattern is presented that can be used in the construction of a band matrix from spectral data. The procedure allows for the stable O (n-sq) construction of a real symmetric band matrix having specified eigenvalues and first p components of its normalized eigenvectors. The procedure can also be used in the second phase of the construction of a band matrix from the interlacing eigenvalues. Previously presented algorithms for these reductions using elementary orthogonal similarity transformations require O (n- cubed) arithmetic operations. Keywords: Band matrix, Inverse eigenvalue problem, Givens rotations.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1988
Accession Number
ADA204178

Entities

People

  • Gregory Ammar
  • William Gragg

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Air Platforms
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Arithmetic
  • Computations
  • Eigenvalues
  • Eigenvectors
  • Identities
  • Illinois
  • Interlacing
  • Mathematical Analysis
  • Mathematics
  • Numbers
  • Real Numbers
  • Rotation
  • Schools
  • Security
  • Universities

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Phased Array Antenna Design.