Implementation of sparse matrix in Cholesky decomposition to solve normal equation.

Abstract

Practical measurement schemes require redundant observations for quality control and errors checking. This led to inconsistent solution where every subset (minimum required data) gives different results. Least Square Estimation (LSE) is a method to provide a unique solution (of the normal equation) from redundant observations by minimizing the sum of squares of the residuals. Analysis of LSE also provide estimate quality of parameters, observations and residuals, assessment of network’s reliability and precision, detection of gross errors etc. Many methods can be applied to solve normal equation, e.g. Gauss-Doolittle, Gauss-Jordan Elimination, Singular Value Decomposition, Iterative Jacoby etc. Cholesky Decomposition is an efficient method to solve normal equation with positive definite and symmetric coefficient matrix. It is also capable of detecting weak condition 1 of the system. Solving large normal equation will require a lot of times and computer memory. Implementation of sparse matrix in Cholesky Decomposition will speed up the execution times and minimize the memory usage by exploiting the zeros and symmetrical of coefficient matrix. This paper discusses the procedures and benefits of implementing sparse matrix in Cholesky Decomposition. Some preliminary results are also included.