This paper presents a new algorithm for computing the transfer function from state equations for linear system. This algorithm employs an approximation method, which uses Krylov subspace techniques for linear system. We have focused on the Lanczos-based using the properties of Schur complemnts. This approach reduces the computation of transfer function from state equation for linear system.
This paper presents a simple unifying algorithm for iterative methods that use two Krylov subspaces. This new approach leads us to a general algorithm called the bi-recursive interpolation algorithm (Bi-RIA), which is a generalization of the recursif interpolation algorithm (RIA), the Bi-RIA includes the iterative methods of Lanczos type using two auxilary vectors. We will show how to choose two free sets of parameters and one matrix in the Bi-RIA for recovering known iterative methods of Lanczos type. Other choices of these parameters yield some new methods.
This paper presents a new algorithm of Lanczos method for solving a nonsymmetric systems of linear equations. This algorithm uses an other way of implemtation of this method. We have focused on the Lanczos biorthogonalization procedure using the properties of Schur complemnts and the properties of linear algebra for give this work. We compared this algorithm with GMRS, BiCG and BiCGStab.
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