Accession Number:

AD0744970

Title:

Calculating the Eigenvectors of Diagonally Dominant Matrices,

Descriptive Note:

Corporate Author:

TEXAS UNIV AUSTIN CENTER FOR NUMERICAL ANALYSIS

Personal Author(s):

• Blevins,M. M.
• Stewart,G. W.

Report Date:

1972-06-01

Pagination or Media Count:

26.0

Abstract:

The paper proposes an algorithm for calculating the eigenvectors of a diagonally dominant matrix all of whose elements are known to high relative accuracy. Eigenvectors corresponding to pathologically close eigenvalues are treated by computing the invariant subspace that they span. If the off-diagonal elements of the matrix are sufficiently small, the method is superior to standard techniques, and indeed it may produce a complete set of eigenvectors with an amount of work proportional to the square of the order of the matrix. An analysis of the effects of perturbations in the matrix on the eigenvectors is given. Author

Descriptors:

• (*MATRICES(MATHEMATICS)
• ALGORITHMS)
• TRANSFORMATIONS(MATHEMATICS)
• OPERATORS(MATHEMATICS)
• PERTURBATION THEORY
• ITERATIONS
• THEOREMS

Subject Categories:

• Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE