Stability Analysis Of Continuous Conjugate Gradient Method
Kaedah Conjugate Gradient adalah sangat berguna untuk: menyelesaikan masalah tiada kekangan paling optimum yang berskala besar. Walaubagaimanapun, carlan garis (line search) dalam Kaedah Conjugate Gradient kadang-kadang sukar didapati dan pengiraannya menggunakan komputer adalah sangat mahal. Ber...
| Main Author: | |
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| Format: | Thesis |
| Language: | English |
| Published: |
2008
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| Subjects: | |
| Online Access: | http://eprints.usm.my/31087/1/NURZALINA_BINTI_HARUN.pdf |
| _version_ | 1825832471131848704 |
|---|---|
| author | Harun, Nurzalina |
| author_facet | Harun, Nurzalina |
| author_sort | Harun, Nurzalina |
| collection | USM |
| description | Kaedah Conjugate Gradient adalah sangat berguna untuk: menyelesaikan masalah
tiada kekangan paling optimum yang berskala besar. Walaubagaimanapun, carlan
garis (line search) dalam Kaedah Conjugate Gradient kadang-kadang sukar didapati
dan pengiraannya menggunakan komputer adalah sangat mahal. Berdasarkan
penyelidikan oleh Sun dan Zhang [J. Sun and J. Zhang (2001), Global convergence
of conjugate gradient methods without line search], menyatakan bahawa Kaedah
Conjugate Gradient adalah menumpu secara global (globally convergence) dengan
menggunakan langkah (stepsize) ak yang ditetapkan berdasarkan formula
8r/ ft. Darlpada keputusan yang didapati, mereka mencadangkan carlan
Ilpkll{4
garis (line search) adalah tidak diperlukan untuk mendapatkan penumpuan secara
global (globally convergence) oleh Kaedah Conjugate Gradient. Oleh itu, objektif
disertasi ini adalah untuk menentukan julat a dan P di mana julat ini akan
memastikan kestabilan Kaedah Conjugate Gradient.
In order to solve a large-scale unconstrained optimization, Conjugate Gradient
Method has been proven to be successful. However, the line search required in
Conjugate Gradient Method is sometimes extremely difficult and computationally
expensive. Studies conducted by Sun and Zhang [J. Sun and J. Zhang (2001), Global
convergence of conjugate gradient methods without line search], claimed that the
Conjugate Gradient Method was globally convergence using "fixed" stepsize at
determined using formula at = 8rk
T fk . The result suggested that for global
Ilpkl~
convergence of Conjugate Gradient Method, line search was not compUlsory.
Therefore, tlfts dissertation's objective is to determine the range of a and P where
this range will ensure the stability of Conjugate Gradient Method. |
| first_indexed | 2024-03-06T14:53:21Z |
| format | Thesis |
| id | usm.eprints-31087 |
| institution | Universiti Sains Malaysia |
| language | English |
| last_indexed | 2024-03-06T14:53:21Z |
| publishDate | 2008 |
| record_format | dspace |
| spelling | usm.eprints-310872016-11-15T03:23:23Z http://eprints.usm.my/31087/ Stability Analysis Of Continuous Conjugate Gradient Method Harun, Nurzalina QA1 Mathematics (General) Kaedah Conjugate Gradient adalah sangat berguna untuk: menyelesaikan masalah tiada kekangan paling optimum yang berskala besar. Walaubagaimanapun, carlan garis (line search) dalam Kaedah Conjugate Gradient kadang-kadang sukar didapati dan pengiraannya menggunakan komputer adalah sangat mahal. Berdasarkan penyelidikan oleh Sun dan Zhang [J. Sun and J. Zhang (2001), Global convergence of conjugate gradient methods without line search], menyatakan bahawa Kaedah Conjugate Gradient adalah menumpu secara global (globally convergence) dengan menggunakan langkah (stepsize) ak yang ditetapkan berdasarkan formula 8r/ ft. Darlpada keputusan yang didapati, mereka mencadangkan carlan Ilpkll{4 garis (line search) adalah tidak diperlukan untuk mendapatkan penumpuan secara global (globally convergence) oleh Kaedah Conjugate Gradient. Oleh itu, objektif disertasi ini adalah untuk menentukan julat a dan P di mana julat ini akan memastikan kestabilan Kaedah Conjugate Gradient. In order to solve a large-scale unconstrained optimization, Conjugate Gradient Method has been proven to be successful. However, the line search required in Conjugate Gradient Method is sometimes extremely difficult and computationally expensive. Studies conducted by Sun and Zhang [J. Sun and J. Zhang (2001), Global convergence of conjugate gradient methods without line search], claimed that the Conjugate Gradient Method was globally convergence using "fixed" stepsize at determined using formula at = 8rk T fk . The result suggested that for global Ilpkl~ convergence of Conjugate Gradient Method, line search was not compUlsory. Therefore, tlfts dissertation's objective is to determine the range of a and P where this range will ensure the stability of Conjugate Gradient Method. 2008-06 Thesis NonPeerReviewed application/pdf en http://eprints.usm.my/31087/1/NURZALINA_BINTI_HARUN.pdf Harun, Nurzalina (2008) Stability Analysis Of Continuous Conjugate Gradient Method. Masters thesis, Universiti Sains Malaysia. |
| spellingShingle | QA1 Mathematics (General) Harun, Nurzalina Stability Analysis Of Continuous Conjugate Gradient Method |
| title | Stability Analysis Of Continuous
Conjugate Gradient Method
|
| title_full | Stability Analysis Of Continuous
Conjugate Gradient Method
|
| title_fullStr | Stability Analysis Of Continuous
Conjugate Gradient Method
|
| title_full_unstemmed | Stability Analysis Of Continuous
Conjugate Gradient Method
|
| title_short | Stability Analysis Of Continuous
Conjugate Gradient Method
|
| title_sort | stability analysis of continuous conjugate gradient method |
| topic | QA1 Mathematics (General) |
| url | http://eprints.usm.my/31087/1/NURZALINA_BINTI_HARUN.pdf |
| work_keys_str_mv | AT harunnurzalina stabilityanalysisofcontinuousconjugategradientmethod |