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

Setan, Halim and Asyran, Muhammad (2005) Implementation of sparse matrix in Cholesky decomposition to solve normal equation. In: International Symposium & Exhibition on Geoinformation 2005 Geospatial Solutions for Managing the Borderless World,, 27 – 29.9.05., Pulau Pinang.

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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.

Item Type:Conference or Workshop Item (Paper)
Uncontrolled Keywords:Least Square Estimation, Bordering Method, STARNET
Subjects:T Technology > TA Engineering (General). Civil engineering (General)
Divisions:Geoinformation Science And Engineering (Formerly known)
ID Code:1218
Deposited By: En. Tajul Ariffin Musa
Deposited On:01 Mar 2007 02:55
Last Modified:01 Jun 2010 02:52

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