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On the properties of matrices defining some classes of BVMs

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Summary

It is known that the matrices defining the discrete problem generated by a k-step Boundary Value Method (BVM) have a quasi-Toeplitz band structure [7]. In particular, when the boundary conditions are skipped, they become Toeplitz matrices. In this paper, by introducing a characterization of positive definiteness for such matrices, we shall prove that the Toeplitz matrices which arise when using the methods in the classes of BVMs known as Generalized BDF and Top Order Methods have such property.

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Authors and Affiliations

  1. Dipartimento di Energetica, Università di Firenze, Via C. Lombroso 6/17, 50134, Firenze, Italy

    Lidia Aceto & Donato Trigiante

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  1. Lidia Aceto
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  2. Donato Trigiante
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Correspondence to Lidia Aceto.

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Mathematics Subject Classification (2000): 65L06, 47B35, 15A48

Work supported by G.N.C.S.

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Aceto, L., Trigiante, D. On the properties of matrices defining some classes of BVMs. Numer. Math. 96, 1–16 (2003). https://doi.org/10.1007/s00211-003-0464-y

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  • DOI: https://doi.org/10.1007/s00211-003-0464-y

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