Sparse Matrix-Vector Multiplication and Conjugate Gradient Algorithm on Hybrid Computing Platforms

The solution to a nonsingular linear system Ax=b lies in a Krylov space whose dimension is the degree of the minimal polynomial of A (where A is a matrix, x & b are vectors). If this minimal polynomial of A has a low degree, a Krylov method has the potential of rapid convergence [1]. When solving a system of linear equations Ax=b, if the coefficient matrix A is large and sparse, the time required to solve the system by direct methods is too high and requires too much storage.