Computer assistance for ``discovering'' formulas in system engineering and operator theory
type: Item
instance of: scholarly article
title: Computer assistance for ``discovering'' formulas in system engineering and operator theory
zbMATH Open document ID: 0924.93011
author: J. William Helton
author: Mark Stankus
published in: Journal of Functional Analysis
publication date: 1999-05-18T00:00:00Z
full work available at URL: https://digitalcommons.calpoly.edu/cgi/viewcontent.cgi
review text: The objective of this paper is twofold. First the authors present in considerable detail a methodology for using a combination of computer assistance and human intervention to discover highly algebraic theorems in operator, matrix, and linear systems engineering theory. Secondly the authors illustrate the methodology by deriving theorems: 1. The Bart-Gohberg-Kaashoek-van Dooren theorem. 2. An \(H^\infty\) control problem theorem. 3. Matrix completion problems. The commands used in deriving these results rely on noncommutative Gröbner Basis algorithms. The reader need not understand this theoretical basis in order to appreciate the derivation of these theorems. However, in the second part of this paper, theory and more details are given. This part contains background on ideals and Gröbner bases and also more details on the commands used in the first part of this paper.
Mathematics Subject Classification ID: 93B40
Mathematics Subject Classification ID: 93B28
Mathematics Subject Classification ID: 93-04
Mathematics Subject Classification ID: 47-04
zbMATH DE Number: 1270850
zbMATH Keywords: \(H^\infty\) control
zbMATH Keywords: matrix completion
zbMATH Keywords: non-commutative Gröbner basis algorithms
zbMATH Keywords: operator theory
zbMATH Keywords: system engineering
zbMATH Keywords: computer assistance
zbMATH Keywords: algebraic theorems
zbMATH Keywords: Bart-Gohberg-Kaashoek-van Dooren theorem
reviewed by: Johannes W. Nieuwenhuis
describes a project that uses: NCAlgebra
MaRDI profile type: Publication
OpenAlex ID: W2041611195
cites work: Minimal factorization of matrix and operator functions
cites work: Completing a block diagonal matrix with a partially prescribed inverse
cites work: Q3994509
cites work: Q4023642
cites work: State-space solutions to standard H/sub 2/ and H/sub infinity / control problems
cites work: Q3808248
cites work: Synergy in the Theories of Gröbner Bases and Path Algebras
cites work: Computer simplification of formulas in linear systems theory
cites work: Q4317807
cites work: An introduction to commutative and noncommutative Gröbner bases
cites work: Q4153620
cites work: Q3668379
cites work: Q4040100
DOI: 10.1006/JFAN.1998.3249
description: scientific article; zbMATH DE number 1270850