Calculation in Parallel Sensitivity Function Using Vector Presentation Algorithm (VPA)

This paper presents a new algorithm to solve in parallel linear equations which represent a mathematical model for a large dimension control system and calculates in parallel sensitivity function using n-1 processors where n is a number of linear equation that can be represented as TX=W, where T is a matrix of size nr nc, X=T-1W ,is a vector of unknowns, and #8706;X/#8706;h=-T-1( (#8706;T/#8706;h)X-(#8706;W/#8706;h)) is a sensitivity function with respect to variation of system components h. The algorithm (VPA) divides the mathematical input model into two partitions and uses only (n-1) processors to find out the vector of unknowns for original system x= (x1,x2,..,xn)T and in parallel using (n-1) processors to find the vector of unknowns for similar system (x|)t=-dtT-1= (x|1,x|2,..,x|n)T where d is a constant vector .Finally, the sensitivity function (with respect to variation of any component #8706;X/#8706;hi = ( xi x|i ) can be calculated in parallel by multiplication unknowns xi x|i respectively, where i=0,1,..n-1 .The running time t is reduced by O(t/2) and the efficiency of (VPA ) is increased by 50-60% .