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Homotopy method for general \(\lambda\)-matrix problems. (English) Zbl 0661.65043

A homotopy method is introduced for the solution of the k-th degree \(\lambda\)-matrix problem \((A_ k\lambda^ k+A_{k-1}\lambda^{k- 1}+...+A_ 1\lambda +A_ 0)x=0\). Smooth curves connecting trivial solutions to desired eigenpairs are shown to exist. The method might be used to find all isolated eigenpairs for large-scale \(\lambda\)-matrix problems on single-instruction multiple data (SIMD) machines.
Reviewer: F.Szidarovszky

MSC:

65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65H10 Numerical computation of solutions to systems of equations
58C99 Calculus on manifolds; nonlinear operators
55M25 Degree, winding number
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