A PCGM algorithm for solving linear equations |
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| Authors: | XIA Lin-lin ZHANG Li and WU Kai-teng |
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| Institution: | College of Mathematics and Soft Science, Sichuan Normal University, Chengdu 610066, P. R. China; Key Laboratory of Numerical Simulation in the Sichuan Provincial College, Neijiang Normal University, Neijiang 641112, P. R. China;Key Laboratory of Numerical Simulation in the Sichuan Provincial College, Neijiang Normal University, Neijiang 641112, P. R. China;Key Laboratory of Numerical Simulation in the Sichuan Provincial College, Neijiang Normal University, Neijiang 641112, P. R. China |
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| Abstract: | Based on the predictor corrector, we developed a new improved gradient method named the predictor corrector gradient algorithm (PCGM), which is useful for solving linear equations with symmetric positive definite of coefficient matrix. To improve the speed of convergence of traditional gradient method, we let values of original iterative formula be viewed as forecast values. Meanwhile, they are corrected by a new iterative formula through introducing corresponding step parameter. Therefore, a feasible and efficient algorithm is constructed. Numerical experiments indicate that PCGM method not only improve the accuracy and the speed of convergence, but also greatly reduce the number of steps to converge. The simple algorithm is easy to be realized and operated. |
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| Keywords: | predictor corrector gradient method symmetric positive definite convergence speed |
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