What you have (shown) is a linear system of equations, with 100 equations and only 9 unknowns. This is exactly what matlab is designed to solve. Since the system is rather overdetermined, 91 more equations than unknowns, it is likely that all equations cannot be solved exactly at the same time, but you should be able to get a least-square solution without problems. What you should do is to create a matrix, M, with the coefficients for each equation row-by-row. After you've done that you have a simple matrix equation:
PGAS_vector = M*ABCDEFGHI;
Where the ABCDEFGHI array is an array with your 9 unknowns, and the PGAS_vector is the column-vector with all your PGASiteCorrectedIntraResidual components. Matlab is expertly designed to solve this type of overdetermined equations:
ABCDEFGHI = M\PGAS_vector;
That way you get a least-square solution for all your 9 unknowns.
Now, if the equations you've not shown contains non-linear terms in the unknowns this is not a solution.
HTH
