Minimization properties and short recurrences (Q1294590)

The paper deals with the problem of solving the linear system \(Ax= b\), where \(A\) is a square, nonsingular and nonsymmetric matrix of dimension \(n\). Step-dependent preconditioned conjugate Krylov subspace methods are used to obtain orthogonalization methods with a short recurrence and a minimization property in a fixed form. Numerical tests for the recurrence length \(l=5\) are given and the performances of the proposed algorithms are compared with state-of-the-art methods.