id: 05989519
dt: j
an: 05989519
au: Kvasov, Boris
ti: Parallel mesh methods for tension splines.
so: J. Comput. Appl. Math. 236, No. 5, 843-859 (2011).
py: 2011
pu: Elsevier Science B.V. (North-Holland), Amsterdam
la: EN
cc: 
ut: shape preserving spline interpolation; hyperbolic and thin plate tension
    splines; superposition principle; parallel Gaussian elimination;
    finite-difference schemes in fractional steps; differential multipoint
    boundary value problem; numerical examples
ci: 
li: doi:10.1016/j.cam.2011.05.019
ab: Summary: This paper addresses the problem of shape preserving spline
    interpolation formulated as a differential multipoint boundary value
    problem (DMBVP). Its discretization by a 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 (successive overrelaxation method and
    finite-difference schemes in fractional steps) and admit effective
    parallelization. Numerical examples illustrate the main features of
    this approach.
rv: