# 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

# Descriptors:

# Subject Categories:

- Theoretical Mathematics