A note on the efficient solution of matrix pencil systems

Algorithms for solving matrix pencil systems of linear equations, of the form (A+B)x=c+d, are developed and analysed. The techniques that are discussed are based on methods for the generalized eigenvalue problem and avoid refactoring a matrix when the scalar changes. Numerical results are presented which demonstrate the advantages of the new techniques.The work of the first author was supported by the National Research Council of Canada and that of the second author by the National Science Foundation under Grant # MCS 76-24433.