Interpolatory tension splines with automatic selection of tension factors
SIAM Journal on Scientific and Statistical Computing
An algorithm for constructing convexity and monotonicity-preserving splines in tension
Computer Aided Geometric Design
Journal of Approximation Theory
Interpolation with exponential B-splines in tension
Geometric modelling
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Spline curves and surfaces with tension
An international conference on curves and surfaces on Wavelets, images, and surface fitting
Sharp error bounds for interpolating splines in tension
Journal of Computational and Applied Mathematics
A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures
Journal of the ACM (JACM)
A generalized curve subdivision scheme of arbitrary order with a tension parameter
Computer Aided Geometric Design
A subdivision scheme for surfaces of revolution
Computer Aided Geometric Design
A shape-preserving approximation by weighted cubic splines
Journal of Computational and Applied Mathematics
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This paper addresses the problem of shape preserving spline interpolation formulated as a differential multipoint boundary value problem (DMBVP for short). Its discretization by mesh method yields a five-diagonal linear system which can be ill-conditioned for unequally spaced data. Using the superposition principle we split this system in a set of tridiagonal linear systems with a diagonal dominance. The latter ones can be stably solved either by direct (Gaussian elimination) or iterative methods (SOR method and finite-difference schemes in fractional steps) and admit effective parallelization. Numerical examples illustrate the main features of this approach.