Chu, Moody T.; Li, T. Y.; Sauer, Tim Homotopy method for general \(\lambda\)-matrix problems. (English) Zbl 0661.65043 SIAM J. Matrix Anal. Appl. 9, No. 4, 528-536 (1988). 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 Cited in 9 Documents 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 Keywords:zeros of polynomial systems; lambda-matrix; single-instruction multiple data machines; homotopy method; eigenpairs PDFBibTeX XMLCite \textit{M. T. Chu} et al., SIAM J. Matrix Anal. Appl. 9, No. 4, 528--536 (1988; Zbl 0661.65043) Full Text: DOI