ABSTRACT
Instead of solving system by a direct method, e.g., by Gaussian elimination, in many cases it may be advantageous to use an iterative method of solution. This is particularly true when the dimension n of system is very large, and unless a special fast algorithm such as FFT can be employed, the O(n3) cost of a direct method would be unbearable. This chapter describes some popular iterative methods, and outlines the conditions under which it may be advisable to use an iterative method rather than a direct method, or to prefer one particular iterative method over another. It presents examples where the Jacobi method, the Gauss-Seidel method, and the Over-Relaxation methods are outlined. The chapter discusses the Richardson method and Chebyshev iterations and conjugate gradients.
