Fundamentals of matrix computations
Fundamentals of matrix computations
Numerical analysis: mathematics of scientific computing
Numerical analysis: mathematics of scientific computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Sequential iterations for two diagonal preconditioners
Computers & Mathematics with Applications
A generalization of the optimal diagonal approximate inverse preconditioner
Computers & Mathematics with Applications
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We introduce two diagonal preconditioners, one of them is a scaling of the matrix. They are obtained by minimizing the norm of the iteration matrix using the Frobenius and @?"~ norms. We prove convergence of the corresponding iterations for the class of diagonally dominant matrices. For the @?"~ iteration, we also prove convergence for positive definite matrices. Both iterations compete very well with the Jacobi iteration.