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**Parallel Calculation Sensitivity Function for Multi Tasking Environments**

Hamed Al Rjoub and Ahmed Al-Sha'or

**DOI : **10.3844/jcssp.2010.75.79

*Journal of Computer Science*

Volume 6, Issue 1

Pages 75-79

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**Abstract**

**Problem statement:** Calculating sensitive functions for a large dimension control system to find the unknowns vectors for a linear system in both single and multi processors, is not considered internally compatible with multi tasking environments, so breaking the process can cost time and memory and it couldn't be paused, resumed and saved as patterns for later continuity. This study is an attempt to solve this problem in parallel to reduce the time factor needed and increase the efficiency by using parallel calculation sensitivity function for multi tasking environments (PSME) algorithm. **Approach:** calculate in parallel sensitivity function using n-1 processors where n is a number of linear equations which can be represented as TX = W, where T is a matrix of size n_{1}×n_{2}, X = T^{-1}W, is a vector of unknowns and ∂X/∂h = T^{-1}((∂T/∂h)-(∂W/∂h)) is a sensitivity function with respect to variation of system components h. The algorithm (PSME) divides the mathematical input model into two partitions and uses only (n-1) processors to find the vector of unknowns for original system x = (x_{1},x_{2},…,x_{n})^{T} and in parallel using (n-1) processors to find the vector of unknowns for similar system (x’)^{t} = d^{t}T^{-1} = (x_{1}’,x_{2}’,…x_{n}’)^{T} by using Net-Processors, where d is a constant vector. Finally, sensitivity function (with respect to variation of component ∂X/∂h_{i} = (x_{i}×x_{i}’) can be calculated in parallel by multiplication unknowns X_{i}×X_{i}’, where i = 0,1,…n-1. **Results:** The running time t is reduced to O(t/n-1) and, the performance of (PSME) was increased by 30-40%. **Conclusion**: Hence, used (PSME) algorithm reduced the time to calculate sensitivity function for a large dimension control system and the performance was increased.

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**Copyright**

© 2010 Hamed Al Rjoub and Ahmed Al-Sha'or. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.