Istituto di Matematica Applicata e Tecnologie Informatiche     
Simoncini V. Linear systems with a quadratic parameter and application to structural dynamics. Preprint ercim.cnr.ian//1998-1111, 1998.
The numerical solution of the linear system $(sigma^2 A + sigma B + C) x = b,$ where $A, B$ and $C$ are large complex Hermitian or symmetric matrices of size $n$, $b, x$ vectors of length $n$ and $sigmain CC$, arises in important applications. In this paper we explore a symmetric formulation that allows to efficiently solve the system for several values of $sigma$ simultaneously, by means of a short-term recurrence method. Numerical experiments on structural dynamic problems report on the improvement of the new approach over existing methods.
Subject Iterative methods, quadratic parameter, QMR, J--symmetric linear systems, complex symmetric matrices.

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