Fast imaginary matrix inversion

Hello everybody, in the script I´m developing I have to deal with the inversion of an imaginary square matrix which dimensions are in the order of 10e3x10e3, therefore it is very huge. Although the inversion is performed with the "\" function, from the timing report I noticed that it is extremely time consuming, expecially considering that it is running in a for loop which lasts 10 iterations. The matrix to be inverted is Z = (R+jwL) where R is a diagonal matrix, L is a symmetric matrix, j is the imaginary unit and w is the the frequency (which change with each iteration). I need to speed up the script, therefore could anyone suggest me a way to speed up and/or simplify this inversion?

Thank you in advance!

[Aveek Podder]

As R is diagonal and L is a symmetric matrix. Assuming the inverse to be (A + jB) and equating Z*(A + jB) to an identity matrix. Will give:

B = -inv(R)*(wL)*A
A = inv(R-(wL)*inv(R)*(wL))

Hope this simplifies the inverse.