A Maple Package for the Symbolic Computation of Drazin Inverse Matrices with Multivariate Transcendental Functions Entries

2020 ◽  
pp. 156-170
Author(s):  
Jorge Caravantes ◽  
J. Rafael Sendra ◽  
Juana Sendra
Keyword(s):  
Symbolic Computation ◽  
Drazin Inverse ◽  
Transcendental Functions ◽  
Maple Package

scholarly journals Generalized inversion by interpolation

Filomat ◽  
2007 ◽  
Vol 21 (1) ◽  
pp. 67-86 ◽  
Author(s):  
Predrag Stanimirovic ◽  
Milan Tasic ◽  
Predrag Krtolica ◽  
Nikolas Karampetakis
Keyword(s):  
Programming Languages ◽  
Symbolic Computation ◽  
Polynomial Matrix ◽  
Drazin Inverse ◽  
Generalized Inversion ◽  
Procedural Programming ◽  
Programming Package

We investigate two algorithms for computing the Moore-Penrose and Drazin inverse of a given one-variable polynomial matrix by interpolation. These algorithms differ in the method used for constant matrices inverses computing. The first algorithm uses the Grevile?s method, and the second one uses the Leverrier-Faddeev method and its generalization. These algorithms are especially useful for symbolic computation in procedural programming languages. We compare results by implementing the algorithms in the programming package MATHEMATICA and in the procedural programming languages DELPHI and C++.

Symbolic computation to estimate two-sided boundary conditions in two-dimensional conduction problems

10.2514/3.920 ◽  
1997 ◽  
Vol 11 ◽  
pp. 472-476
Author(s):  
Henry H. Kerr ◽  
F. C. Frank ◽  
Jae-Woo Lee ◽  
W. H. Mason ◽  
Ching-Yu Yang
Keyword(s):  
Boundary Conditions ◽  
Symbolic Computation ◽  
Two Dimensional

Cline’s formula for g-Drazin inverses in a ring

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2249-2255
Author(s):  
Huanyin Chen ◽  
Marjan Abdolyousefi
Keyword(s):  
Operator Theory ◽  
Spectral Properties ◽  
Associative Ring ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Cline’S Formula

It is well known that for an associative ring R, if ab has g-Drazin inverse then ba has g-Drazin inverse. In this case, (ba)d = b((ab)d)2a. This formula is so-called Cline?s formula for g-Drazin inverse, which plays an elementary role in matrix and operator theory. In this paper, we generalize Cline?s formula to the wider case. In particular, as applications, we obtain new common spectral properties of bounded linear operators.

scholarly journals Simultaneous Contour Method of a Trigonometric Integral by Prudnikov et al.

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1453
Author(s):  
Robert Reynolds ◽  
Allan Stauffer
Keyword(s):  
Closed Form ◽  
Contour Method ◽  
Substantial Part ◽  
Exponential Functions ◽  
Closed Form Solutions ◽  
Definite Integrals ◽  
Transcendental Functions ◽  
Trigonometric Integral

In this present work we derive, evaluate and produce a table of definite integrals involving logarithmic and exponential functions. Some of the closed form solutions derived are expressed in terms of elementary or transcendental functions. A substantial part of this work is new.

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