𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Another Proof of the Total Positivity of the Discrete Spline Collocation Matrix

✍ Scribed by Avraham A. Melkman

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
245 KB
Volume
84
Category
Article
ISSN
0021-9045

No coin nor oath required. For personal study only.

✦ Synopsis

We provide a different proof for Morken's result on necessary and sufficient conditions for a minor of the discrete B-spline collocation matrix to be positive and supply intuition for those conditions.

1996 Academic Press, Inc.

Denote, further,

πŸ“œ SIMILAR VOLUMES

On Total Positivity of the Discrete Spli
On Total Positivity of the Discrete Spline Collocation Matrix
✍ Knut M. MΓΈrken πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 639 KB

R. Q. Jia (J. Approx. Theory 39 (1983), 11 23), proved that the discrete spline collocation matrix was totally positive, and he also gave necessary and sufficient conditions for when a minor has a positive determinant. By a counterexample, it is shown in this paper that his necessary and sufficient

A direct proof for the matrix decomposit
A direct proof for the matrix decomposition of chordal-structured positive semidefinite matrices
✍ Naonori Kakimura πŸ“‚ Article πŸ“… 2010 πŸ› Elsevier Science 🌐 English βš– 116 KB

Agler, Helton, McCullough, and Rodman proved that a graph is chordal if and only if any positive semidefinite (PSD) symmetric matrix, whose nonzero entries are specified by a given graph, can be decomposed as a sum of PSD matrices corresponding to the maximal cliques. This decomposition is recently