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A Method to Find Weight Matrices Having Symmetric Second-Order Differential Operators with Matrix Leading Coefficient

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Abstract

We develop a method to construct examples of weight matrices of size N×N having symmetric second-order differential operators of the form

$$D^{2}A_{2}(t)+D^{1}A_{1}(t)+D^{0}A_{0},$$

where A 2, A 1 and A 0 are matrix polynomials of degrees not larger than 2, 1 and 0, respectively. The main feature of this method is that in some cases it finds weight matrices having such differential operators even though none of these operators has diagonal leading coefficient.

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Authors and Affiliations

  1. Departamento de Análisis Matemático, Universidad de Sevilla, Apdo (P.O. BOX) 1160, 41080, Sevilla, Spain

    Antonio J. Durán

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  1. Antonio J. Durán
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Correspondence to Antonio J. Durán.

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Communicated by Edward B. Saff.

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Durán, A.J. A Method to Find Weight Matrices Having Symmetric Second-Order Differential Operators with Matrix Leading Coefficient. Constr Approx 29, 181–205 (2009). https://doi.org/10.1007/s00365-008-9038-7

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  • DOI: https://doi.org/10.1007/s00365-008-9038-7

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