Volker Strassen first suggested an algorithm to multiply matrices with
worst case running time less than the conventional O(n^3) operations in 1969. He also presented a recursive algorithm with which to invert matrices, and calculate determinants using matrix multiplication. James R. Bunch & John E. Hopcroft improved upon this in 1974 by providing modifications to the inversion algorithm in the case where principal submatrices were singular, amongst other improvements. We cover the case of multivariate polynomial matrix inversion, where it is noted that conventional methods that assume a field will experience major setbacks. Initially, there existed a presentation of a fraction free formulation of inversion via matrix multiplication along with motivations in [TDS17], however analysis of this presentation was rudimentary. We hence provide a discussion of the true complexities of this fraction free method arising from matrix multiplication, and arrive at its limitations.
Original language  English 

Media of output  arxiv.org 

Publication status  Published  3 Jan 2019 

 Matrix Inversion
 Symbolic Computation
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@misc{2c944877a69b441992d4c1aa926f49b8,
title = "On Fast Matrix Inversion by Fast Matrix Multiplication",
abstract = "Volker Strassen first suggested an algorithm to multiply matrices with worst case running time less than the conventional O(n^3) operations in 1969. He also presented a recursive algorithm with which to invert matrices, and calculate determinants using matrix multiplication. James R. Bunch & John E. Hopcroft improved upon this in 1974 by providing modifications to the inversion algorithm in the case where principal submatrices were singular, amongst other improvements. We cover the case of multivariate polynomial matrix inversion, where it is noted that conventional methods that assume a field will experience major setbacks. Initially, there existed a presentation of a fraction free formulation of inversion via matrix multiplication along with motivations in [TDS17], however analysis of this presentation was rudimentary. We hence provide a discussion of the true complexities of this fraction free method arising from matrix multiplication, and arrive at its limitations.",
keywords = "Matrix Inversion, Symbolic Computation",
author = "Zak Tonks",
year = "2019",
month = "1",
day = "3",
language = "English",
type = "Other",
}
TY  GEN
T1  On Fast Matrix Inversion by Fast Matrix Multiplication
AU  Tonks, Zak
PY  2019/1/3
Y1  2019/1/3
N2  Volker Strassen first suggested an algorithm to multiply matrices with
worst case running time less than the conventional O(n^3) operations in 1969. He also presented a recursive algorithm with which to invert matrices, and calculate determinants using matrix multiplication. James R. Bunch & John E. Hopcroft improved upon this in 1974 by providing modifications to the inversion algorithm in the case where principal submatrices were singular, amongst other improvements. We cover the case of multivariate polynomial matrix inversion, where it is noted that conventional methods that assume a field will experience major setbacks. Initially, there existed a presentation of a fraction free formulation of inversion via matrix multiplication along with motivations in [TDS17], however analysis of this presentation was rudimentary. We hence provide a discussion of the true complexities of this fraction free method arising from matrix multiplication, and arrive at its limitations.
AB  Volker Strassen first suggested an algorithm to multiply matrices with
worst case running time less than the conventional O(n^3) operations in 1969. He also presented a recursive algorithm with which to invert matrices, and calculate determinants using matrix multiplication. James R. Bunch & John E. Hopcroft improved upon this in 1974 by providing modifications to the inversion algorithm in the case where principal submatrices were singular, amongst other improvements. We cover the case of multivariate polynomial matrix inversion, where it is noted that conventional methods that assume a field will experience major setbacks. Initially, there existed a presentation of a fraction free formulation of inversion via matrix multiplication along with motivations in [TDS17], however analysis of this presentation was rudimentary. We hence provide a discussion of the true complexities of this fraction free method arising from matrix multiplication, and arrive at its limitations.
KW  Matrix Inversion
KW  Symbolic Computation
M3  Other contribution
ER 