Accession Number:

ADA050976

Title:

Some New Methods for Solving Linear Equations.

Descriptive Note:

Interim rept.,

Corporate Author:

STANFORD UNIV CALIF INFORMATION SYSTEMS LAB

Personal Author(s):

Report Date:

1976-05-01

Pagination or Media Count:

18.0

Abstract:

It takes of the order of N-cubed operations to solve a set of N linear equations in N unknowns. When the underlying physical problem has some time- or shift-invariance properties, the coefficient matrix is of Toeplitz or difference or convolution type and the equations can be with ON-squared operations. We have shown that with any nonsingular N x N matrix, we can associate an integer alpha between 1 and N such that it takes ON-squared alpha operations to invert the matrix. The number alpha may be small for many non-Toeplitz matrices of physical interest. Some aspects of this result are discussed here, including extensions to continuous time kernels and integral equations. Author

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE