Leapfrog variants of iterative methods for linear algebraic equations
Let be \(x^{(i)}\) the sequence generated by an iterative method to solve the real or complex linear system \(Ax=b\). A leapfrog method is a variant such that \(x^{(i)}\) can be expressed directly in terms of \(x^{(i- 2)}\), and a grand-leap method expresses \(x^{(i)}\) directly by \(x^{(0)}\) without computation of intermediate iterates. These two methods are considered for Richardson's method, in particular for the Chebyshev case, and for a general second order method. Six different algorithms are presented and discussed, they include the calculation of the required parameters. The advantages of the methods concerning their efficiency on supercomputers are pointed out.
scientific article; zbMATH DE number 4078625
scientific article