Stability Analysis Of Continuous Conjugate Gradient Method
| dc.contributor.author | HARUN, NURZALINA | |
| dc.date.accessioned | 2016-10-31T09:09:31Z | |
| dc.date.available | 2016-10-31T09:09:31Z | |
| dc.date.issued | 2008-06 | |
| dc.description.abstract | 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. Range for P is obtained from research work done by Torii & Hagan (2002) and Bhaya & Kaszkurewicz (2003). In order to establish the range for a, the coefficient matrix of the system A~ = !!. was assumed to be symmetric positive-definite n x n autocorrelation matrix of a Markov-l input signal for case p = O. This was done by using the continuous realization of the Conjugate Gradient Method iteration which took the fonn of an autonomous system of differential equation. The resulting range of a and p was then simulated to demonstrate the convergence for the system A~ = !!. on the stationary as well as nonstationary Conjugate Gradient Method. For nonstationary Conjugate Gradient Method, A and b were varied with time. Based on the simulation test, convergence of the Conjugate Gradient Method was established for Q and p within the obtained range whi~n confirms the stability of Conjugate Gradient Method. The simulation verify that the stability range also holds for p > 0 . | en_US |
| dc.identifier.uri | http://hdl.handle.net/123456789/2931 | |
| dc.subject | Stability Analysis Of Continuous | en_US |
| dc.subject | Conjugate Gradient Method | en_US |
| dc.title | Stability Analysis Of Continuous Conjugate Gradient Method | en_US |
| dc.type | Thesis | en_US |
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