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University of Regina Department of Mathematics and Statistics

University of Regina
Department of Mathematics and Statistics
Speaker: Dr. Chun-Hua Guo
University of Regina
Title: A Schur­Newton method for the principal pth root of a matrix
Date: Friday, April 07, 2006
Time: 3:30 p.m.
Place: Math & Stats Lounge (CW 307.20)
Let A be a square matrix with no nonpositive real eigenvalues, and p 2
be an integer. The principal pth root of A is denoted by A1/p, which is
the unique matrix X such that Xp = A and the eigenvalues of X lie in the
segment { z : -/p < arg(z) < /p }. The principal inverse pth root A-1/p
can be defined similarly.
When the Newton iteration is applied to the matrix equation X-p -A =
0, with an initial guess X0 commuting with A, the Newton iterates Xk can
be obtained without matrix inversions. We report that if X0 = c-1I for
c > 0 then the iteration converges quadratically to A-1/p if the eigenvalues
of A lie in a wedge-shaped convex set containing the disc { z : |z -cp| < cp }.


Source: Argerami, Martin - Department of Mathematics and Statistics, University of Regina


Collections: Mathematics