Open AccessJournal Article
Iterated parallel diagonal dominant algorithm for tridiagonal systems
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TL;DR: Based on the complexity analysis of the iterative and non-iterative PDD algorithm, the increase of iterative algorithm computational complexity is very small, but the communication complexity increases exponentially with the iteration number.
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Abstract: In parallel solving weak diagonal dominant tridiagonal systems,the approximate error of the Parallel Diagonal Dominant(PDD) algorithm cannot be ignored.An iterated PDD algorithm was presented.In the algorithm,the solution of the correction value was calculated by iterative method,and the computational accuracy was obviously improved.Through error analysis on the algorithm,an estimation formula of iteration number was derived for a given error tolerance.And the numerical experiment shows the validity.Based on the complexity analysis of the iterative and non-iterative PDD algorithm,the increase of iterative algorithm computational complexity is very small,but the communication complexity increases exponentially with the iteration number.
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Citations
Research on Two Algorithms of Solving Large-scale Tridiagonal Linear Equations
Yu Bencheng,Chen Yan +1 more
- 01 Jan 2013
TL;DR: It is shown that the principle of the linear interpolation method and double parameter method is consistent and it points out that in this principle, the solutions to certain types of tridiagonal equations in the two methods are not stable.
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References
Research on Two Algorithms of Solving Large-scale Tridiagonal Linear Equations
Yu Bencheng,Chen Yan +1 more
- 01 Jan 2013
TL;DR: It is shown that the principle of the linear interpolation method and double parameter method is consistent and it points out that in this principle, the solutions to certain types of tridiagonal equations in the two methods are not stable.
2