A limited survey of various conjugate gradient methods for solving complex matrix equations arising in electromagnetic wave interactions

There exists a wide variety of conjugate gradient algorithms for solving the complex matrix equations arising in electromagnetic wave interactions. The objective of this paper is to describe several of these algorithms which we have found to be computationally efficient. Both the strong and weak points of each version of the conjugate gradient method are presented. The principal conclusion is that at present, there is no single algorithm that provides an efficient solution for all types of problems. The computer programs corresponding to the algorithms discussed in the paper are provided in the Appendix.