Title: An algorithm to compute sets enclosing<i>M</i>-numerical ranges with applications in numerical analysis
Abstract: Abstract One of the possible generalizations of the classical numerical range studied in the literature is the so-called M-numerical range. In this paper we present an algorithm which can be used to construct a polygon V enclosing the M-numerical range of a given square matrix A. The algorithm can be executed such that V encloses the M-numerical range of A tightly. The concept of M-numerical ranges can be used to investigate stability properties of numerical methods for approximating the solution to linear initial value problems. To illustrate our algorithm, we consider a numerical method for a given initial-boundary value problem. A modified version of our algorithm will be used to obtain sufficient conditions for the stability of the numerical method under consideration. ∗Most of this research has been carried out at the Department of Mathematics and Computer Science, University of Leiden, The Netherlands, with Support of the Netherlands Organization for Scientific Research (N.W.O.). Submitted in conjunction with the Second Workshop on Numerical Ranges and Numerical Radii held in August 1994 at the University of Coimbra, Portugal. ∗Most of this research has been carried out at the Department of Mathematics and Computer Science, University of Leiden, The Netherlands, with Support of the Netherlands Organization for Scientific Research (N.W.O.). Submitted in conjunction with the Second Workshop on Numerical Ranges and Numerical Radii held in August 1994 at the University of Coimbra, Portugal. Notes ∗Most of this research has been carried out at the Department of Mathematics and Computer Science, University of Leiden, The Netherlands, with Support of the Netherlands Organization for Scientific Research (N.W.O.). Submitted in conjunction with the Second Workshop on Numerical Ranges and Numerical Radii held in August 1994 at the University of Coimbra, Portugal.
Publication Year: 1996
Publication Date: 1996-07-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 2
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