Hyperbolic spline interpolation algorithms

Isogeometric interpolation by hyperbolic splines is formulated as a differential multipoint boundary value problem. A discretization of this problem results in the necessity of solving a linear system with a five-diagonal matrix. This system can be ill-conditioned if the data are nonuniformly distributed. It is shown that this system can be split into tridiagonal systems with the property of diagonal dominance. The latter do not require that hyperbolic functions be evaluated. Their solution is numerically stable and can be efficiently parallelized on the basis of the superposition principle. For quasiuniform grids, these systems have positive definite matrices. Algorithms for parallelizing calculations in the case of tri- and five-diagonal systems are given.