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Conditions of matrices in discrete tension spline approximations of DMBVP

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Abstract

Some splines can be defined as solutions of differential multi-point boundary value problems (DMBVP). In the numerical treatment of DMBVP, the differential operator is discretized by finite differences. We consider one dimensional discrete hyperbolic tension spline introduced in (Costantini et al. in Adv Comput Math 11:331–354, 1999), and the associated specially structured pentadiagonal linear system. Error in direct methods for the solution of this linear system depends on condition numbers of corresponding matrices. If the chosen mesh is uniform, the system matrix is symmetric and positive definite, and it is easy to compute both, lower and upper bound, for its condition. In the more interesting non-uniform case, matrix is not symmetric, but in some circumstances we can nevertheless find an upper bound on its condition number.

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Authors and Affiliations

  1. Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000, Zagreb, Croatia

    Mladen Rogina

  2. Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lučića 5, 10000, Zagreb, Croatia

    Sanja Singer

Authors
  1. Mladen Rogina
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  2. Sanja Singer
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Correspondence to Mladen Rogina.

Additional information

This research was supported by Grant 0037114, by the Ministry of Science, Education and Sports of the Republic of Croatia.

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Rogina, M., Singer, S. Conditions of matrices in discrete tension spline approximations of DMBVP. Ann. Univ. Ferrara 53, 393–404 (2007). https://doi.org/10.1007/s11565-007-0019-8

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  • DOI: https://doi.org/10.1007/s11565-007-0019-8

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