MATRIX BANDWIDTH REDUCTION FOR INTERPOLATION WITH SPLINES IN TENSION

Boundary conditions widen twice a band of a matrix of a system of linear equations that arises in interpolation with splines in tension (a generalization of Briggs’ method). A node numbering scheme of the finite difference mesh that allows significantly narrow the band and reduce a profile of the matrix is proposed. The described 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. Keywords: bandwidth reduction, profile reduction, node numbering scheme, splines in tension, Briggs’ method, banded matrix, cognitive graphics.