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<p>Boundary conditions widen twice the band of the matrix of a system of linear equations in the method of interpolation by splines in tension (a generalization of Briggs’ method). A node numbering scheme for a finite difference grid is proposed, which significantly narrows down the band and reduces the matrix profile. The method belongs to cognitive graphics methods and is not based on graph theory concepts. The scheme or its modifications can be extended to other similar problems.</p>

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Matrix Bandwidth Reduction for Interpolation by Splines in Tension

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • Y. Nazarenko

摘要

Boundary conditions widen twice the band of the matrix of a system of linear equations in the method of interpolation by splines in tension (a generalization of Briggs’ method). A node numbering scheme for a finite difference grid is proposed, which significantly narrows down the band and reduces the matrix profile. The method belongs to cognitive graphics methods and is not based on graph theory concepts. The scheme or its modifications can be extended to other similar problems.