TY - JOUR
TI - COMPUTING CAUCHY INTEGRAL THEOREM OF A MATRIX FUNCTION VIA SIMILARITY TRANSFORMATION AND BEHAVIOR OF HYPERGEOMETRIC MATRIX DENSITY FUNCTION
PY - 2022/12/01
Y2 - 2024/10/03
JF - The Transactions of the Nigerian Association of Mathematical Physics
JA - TNAMP
VL - 18
SE - Articles
UR - https://nampjournals.org.ng/index.php/tnamp/article/view/166
SP - 87-100
AB - It is shown that Cauchy integral matrix function is Lebesgue measurable on the contour integral based on the Little Woodâ€™s third formula for which the trapezoidal rule and Simpson composite method are applicable. As a follow up, it is demonstrated that Taylor series representation of Cauchy integral matrix function is commutable with similarity matrix transformation when Jordan canonical block along diagonal is taken into consideration. The spectrum of the diagonalizable matrix A is computed using the Givensorthogonal matrix plane rotation. As an extension of ideas; a measure of effectiveness on the use of SVD in the computation process is emphasized and fully utilized which leads to demonstration with the exponential of a matrix function as an example. Further analytical reasoning on performance of Cauchy integral theorem for the matrix functional calculus leads to the method of Residue theorem. Thedensity of a matrix function is calculated based on the hypergeometric series taking into consideration the behavior of gamma function.
ER -