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.

Iterated parallel diagonal dominant algorithm for tridiagonal systems

In order to take full use of multi-core technology to enhance the resource utilization of multi-core processors,shorten the execution time and show multi-core system remarkable performance,a multi-threaded parallel program was designed to resolve the tridiagonal equations of odd-even reduction,and the calculation speed of cubic spline curve fitting was increased in multi-core computer.Through comparing the speedup radio of experimental results,it can be seen that parallel program shortens the time of solving equations and multi-core resources are fully utilized.The results indicate that multi-core parallel algorithm of odd-even reduction used in cubic spline curve fitting is effective and feasible and the research results have good practical significance.

Multi-core parallel algorithm for cubic spline curve fitting

Based on the analysis of the two kinds of algorithms in solving large-scale tridiagonal linear equations, which are linear interpolation method and the method of double parameters, 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. But in the case of not so sick, their relative errors of solution are very small, and the situation is very stable.

http://ijcsi.org/papers/IJCSI-10-1-3-378-381.pdf

Research on Two Algorithms of Solving Large-scale Tridiagonal Linear Equations

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Research on Two Algorithms of Solving Large-scale Tridiagonal Linear Equations