University of Regina
Department of Mathematics and Statistics
Speaker: Chun-Hua Guo (University of Regina)
Title: Newton's method and Halley's method for the principal pth root of
Time & Place: Friday, November 21, 3:30 - 4:30 pm, CL 232
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 H-matrices 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.