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Refined Block Conjugate Gradient Method and Its Application

Author: LuXiaoPing
Tutor: GaoWeiGuo
School: Fudan University
Course: Computational Mathematics
Keywords: Symmetric positive definite eigenvalue problem LOBPCG Pre - conditions Self-consistent field iteration
CLC: O241.6
Type: Master's thesis
Year: 2007
Downloads: 89
Quote: 0
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Abstract


Numerical solution of the eigenvalue problem in structural mechanics , electronic physics , molecular biology calculation has very important applications , fast and accurate eigenvalue feature vector is a measure of such a criterion of the numerical methods . Recently, a new subspace iteration method , the pre - conditions of the local optimization block conjugate gradient method ( LOBPCG ) , to its to solving eigenvalue fast high-precision , which is widely used . The numerical results show that the eigenvalues ??convergence , the method is fast and the accuracy is very high , but the results were not good on the corresponding eigenvectors calculated . Based on LOBPCG algorithm ideas, put forward a new subspace iteration method . New method continues the LOBPCG algorithm to to solving eigenvalue rapid high-precision nature , but also makes the corresponding residual norm strictly monotonic convergence , and finally from the numerical experiments to confirm . Nonlinear eigenvalue problem solving , the most commonly used method is iterative self-consistent field ( SCF ) method . The SCF iterative method of feature vector is relatively high precision , in view of the new method can make the residual norm iterative process converges monotonically to consider , and then propose a solution to the nonlinear eigenvalue problem with the self-consistent field iterative method chimeric new ideas . And compared by numerical experiments were observed to better performance results .

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > Linear algebra method of calculating
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