 
Summary: COLLOQUIUM
University of Regina
Department of Mathematics and Statistics
Speaker: ChunHua Guo (University of Regina)
Title: Newton's method and Halley's method for the principal pth root of
a matrix
Time & Place: Friday, November 21, 3:30  4:30 pm, CL 232
Abstract
We present convergence results on Newton's method and Halley's method
for computing the principal pth root of a matrix with no nonpositive real
eigenvalues. We reveal an interesting relationship between Newton/Halley
iteration and the binomial expansion. A few open questions are raised
regarding the positivity/negativity of coefficients in the Taylor expansions
of some special rational functions. Affirmative answer to those questions
will allow better understanding of Newton's method and Halley's method.
We also review a result on the principal pth root of a nonsingular M
matrix and generalize it to nonsingular Hmatrices with positive diagonal
elements. We explain how the principal pth root can be computed by New
ton's method or Halley's method for these special matrices.
