 
Summary: COLLOQUIUM
University of Regina
Department of Mathematics and Statistics
Speaker: Dr. ChunHua 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)
Abstract
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 A1/p
can be defined similarly.
When the Newton iteration is applied to the matrix equation Xp 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 = c1I for
c > 0 then the iteration converges quadratically to A1/p if the eigenvalues
of A lie in a wedgeshaped convex set containing the disc { z : z cp < cp }.
