Successive overrelaxation (SOR) is a method used to solve linear n × n systems of equations, Ax = b. Given the coefficient matrix A, the fight-side vector b, and an initial estimated solution vector x, the algorithm recomputes each x_i based on the x_j (i ≠ j), A, and b. First, write the n equations as 

a₁₁x₁ + a₁₂x₂ + … + a_1nx_n = b₁

a₂₁x₁ + a₂₂x₂ + … + a_2nx_n = b₂

…

a_n1x₁ + a_n2x₂ + … + a_nnx_n = b_n

Arbitrarily use the ith equation to solve for x_i, yielding

x_i = (b_i−a_i1x_i − a_i2x₂ −…− a_inx_n)/a_ii.

Now you can implement SOR on an n process system by having the i^th process compute x_i. Implement an SOR solution using UNIX pipes calls.