Solving System of 2n Equations

[defunc]

Hi there,

I have a system of 2n equations. n of these unknowns can be expressed explicitly in terms of the remaining n. The resulting n x n matrix is more dense than the original 2n x 2n and the original 2n x 2n system has some desired properties like diagonal dominance etc. So, should I leave the 2n equations intact or perform the back substitutions and solve the more complex n equations?

Thanks!

 

[hotvette]

Sounds like you are concerned with computational efficiency and/or accuracy. I think it depends on (1) how big n is and (2) what the condition number is of the matrix in each case. The 2n case will require roughly 8 times the computational resources versus the n case, but if the condition number is more favorable, it might be worth it.