Implementation of sparse matrix in Cholesky decomposition to solve normal equation.
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)...
| Main Authors: | , |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
2005
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| Subjects: | |
| Online Access: | http://eprints.utm.my/1218/ http://eprints.utm.my/1218/1/Paper046Asyran.pdf |
| _version_ | 1848890085655707648 |
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| author | Setan, Halim Asyran, Muhammad |
| author_facet | Setan, Halim Asyran, Muhammad |
| author_sort | Setan, Halim |
| building | UTeM Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-15T20:36:28Z |
| format | Conference or Workshop Item |
| id | utm-1218 |
| institution | Universiti Teknologi Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T20:36:28Z |
| publishDate | 2005 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | utm-12182017-08-29T07:21:38Z http://eprints.utm.my/1218/ Implementation of sparse matrix in Cholesky decomposition to solve normal equation. Setan, Halim Asyran, Muhammad TA Engineering (General). Civil engineering (General) 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. 2005-09 Conference or Workshop Item PeerReviewed application/pdf en http://eprints.utm.my/1218/1/Paper046Asyran.pdf 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 September 2005, Pulau Pinang. http://www.civil.eng.usm.my/isg2005/home.shtml |
| spellingShingle | TA Engineering (General). Civil engineering (General) Setan, Halim Asyran, Muhammad Implementation of sparse matrix in Cholesky decomposition to solve normal equation. |
| title | Implementation of sparse matrix in Cholesky decomposition
to solve normal equation.
|
| title_full | Implementation of sparse matrix in Cholesky decomposition
to solve normal equation.
|
| title_fullStr | Implementation of sparse matrix in Cholesky decomposition
to solve normal equation.
|
| title_full_unstemmed | Implementation of sparse matrix in Cholesky decomposition
to solve normal equation.
|
| title_short | Implementation of sparse matrix in Cholesky decomposition
to solve normal equation.
|
| title_sort | implementation of sparse matrix in cholesky decomposition
to solve normal equation. |
| topic | TA Engineering (General). Civil engineering (General) |
| url | http://eprints.utm.my/1218/ http://eprints.utm.my/1218/ http://eprints.utm.my/1218/1/Paper046Asyran.pdf |