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On Total Positivity of the Discrete Spline Collocation Matrix

✍ Scribed by Knut M. Mørken

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

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✦ Synopsis

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 conditions are not quite correct. The correct form of the theorem is then established.

📜 SIMILAR VOLUMES

Another Proof of the Total Positivity of
Another Proof of the Total Positivity of the Discrete Spline Collocation Matrix
✍ Avraham A. Melkman 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 245 KB

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,