A Preconditioned Precise Integration Method for Solving Ill-Conditioned Linear Equations

FU Minghui; LI Yongxi

doi:10.21656/1000-0887.380206

Volume 39 Issue 4

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FU Minghui, LI Yongxi. A Preconditioned Precise Integration Method for Solving Ill-Conditioned Linear Equations[J]. Applied Mathematics and Mechanics, 2018, 39(4): 462-469. doi: 10.21656/1000-0887.380206

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A Preconditioned Precise Integration Method for Solving Ill-Conditioned Linear Equations

doi: 10.21656/1000-0887.380206

Department of Applied Mechanics and Engineering, Sun Yat-sen University, Guangzhou 510275, P.R.China

Funds: The National Natural Science Foundation of China（11672338;11502172）

Received Date: 2017-07-25
Rev Recd Date: 2017-11-08
Publish Date: 2018-04-15

Abstract

Abstract

In order to reduce the condition number of the coefficient matrix of ill-conditioned linear equations, according to the equilibration thought for matrices, a 1-norm equilibration method was proposed to properly reduce the condition number of the matrix, and expanded to the norm equilibration methods. Then, the norm equilibration method together with the precise integration method was combined for solving ill-conditioned linear equations. The numerical results confirm that, the accuracy, efficiency and application scope of the preconditioned precise integration method for ill-conditioned linear equations all improve significantly (the number of significant digits increases by more than 5 and the number of iterations decreases by about 15). In these methods, the preconditioned precise integration method of 1-norm equilibration is the best.
- norm,
- equilibration,
- preconditioned technology,
- precise integration method,
- ill-conditioned linear equations

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References(15)

References

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