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Parallel homotopy algorithm for symmetric large sparse eigenproblems. (English) Zbl 0839.65048
The homotopy method is applied to solve the eigenproblem $$Ax= \lambda x$$ for real symmetric large sparse matrices $$A$$. That is, a simpler nearby matrix $$D$$ is introduced and its eigenpairs are continuously mapped to those of $$A$$. The problem of choosing an appropriate starting matrix $$D$$ as well as regularity and bifurcation issues for $$\lambda(t)$$ and $$x(t)$$ are discussed. A parallel homotopy algorithm is presented and its performance is compared to that of the Lanczos algorithm.
Reviewer: W.Gander (Zürich)

##### MSC:
 65F15 Numerical computation of eigenvalues and eigenvectors of matrices 65Y05 Parallel numerical computation 65H20 Global methods, including homotopy approaches to the numerical solution of nonlinear equations
##### Software:
EISPACK; SPARSPAK; symrcm; YSMP
Full Text:
##### References:
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