Naslov
Conditions of matrices in discrete tension spline approximations of DMBVP

Autori
Rogina, Mladen ; Singer, Sanja

Izvornik
Annali dell'Università di Ferrara. Sezione 7: Scienze matematiche (0430-3202) 53 (2007), 2; 393-404

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Discrete differential multi-point boundary value problem; Uniform and non-uniform cases; Bounds for condition of the associated linear system

Sažetak
Some splines can be defined as solutions of differential multi-point boundary value problems (DMBVP). In the numerical treatment of DMBVP, the differential operator is discretized by finite differences. We consider one dimensional discrete hyperbolic tension spline introduced in (Costantini et al. in Adv Comput Math 11:331–354, 1999), and the associated specially structured pentadiagonal linear system. Error in direct methods for the solution of this linear system depends on condition numbers of corresponding matrices. If the chosen mesh is uniform, the system matrix is symmetric and positive definite, and it is easy to compute both, lower and upper bound, for its condition. In the more interesting non-uniform case, matrix is not symmetric, but in some circumstances we can nevertheless find an upper bound on its condition number.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA