On the properties of matrices defining some classes of BVMs

Lidia Aceto; Donato Trigiante

doi:10.1007/s00211-003-0464-y

On the properties of matrices defining some classes of BVMs

Lidia Aceto
, Donato Trigiante

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	1-16
Number of pages	16
Journal	Numerische Mathematik
Volume	96
Issue number	1
DOIs	https://doi.org/10.1007/s00211-003-0464-y
Publication status	Published - Nov 2003
Externally published	Yes

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AB - 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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On the properties of matrices defining some classes of BVMs

Abstract

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