An efficient preprocessor for solving systems of linear equations

Abstract

A technique of preprocessing an arbitrary system of linear equations has been presented. The solution scheme comprises two parts-the first reduces the problem to a symmetric positive definite system through multiplying corresponding matrix by its transpose using an algorithm of lower order like Strassen's scheme, and the second uses a standard iterative scheme which, when applied to symmetric positive definite systems, converge to a solution in O(n ²) computation.

Keywords:

• System of linear equations
• positive definite matrix
• matrix multiplication
• preprocessing

C.R.Categories:

• 15A06
• 65B
• 65F