Some New Methods for Solving Linear Equations.
STANFORD UNIV CALIF INFORMATION SYSTEMS LAB
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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
- Theoretical Mathematics