Family of Algorithms for Approximating the Smallest Eigenvalue of a Real Matrixwith No Complex Eigenvalues

摘要

The authors present a family of polynomial-time, quadratically convergentalgorithms for approximating the smallest eigenvalue of a real matrix with no complex eigenvalues. The authors show that Jansen, Roos, and Terlaky's recent path-following algorithm is one member of this family and that the well-known method of applying Newton-Raphson to the characteristic polynomial of the matrix is another. The authors also show that the algorithms can be modified to solve the problem of approximating the smallest root of a polynomial with no complex roots, and they report on the results of some computational tests. (Copyright (c) 1995 by Faculty of Technical Mathematics and Informatics, Delft, The Netherlands.)