Abstract: Previous chapter Next chapter CBMS-NSF Regional Conference Series in Applied Mathematics Cardinal Spline Interpolation4. Cardinal Spline Interpolationpp.33 - 42Chapter DOI:https://doi.org/10.1137/1.9781611970555.ch4PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutExcerpt We deal now with the simplest and most important case of the central problem of these lectures. After a brief analysis of its nature (§ 1), the main results are stated in Theorems 1, 2, 3, below. The proof of uniqueness of solutions in Theorem 1 is based (§ 4) on the eigensplines (5.6) of Lecture 3. The proof of existence of solutions (§ 5) uses the Euler—Frobenius polynomials Πn(t) generated by (1.6) of Lecture 3. Theorem 1 is applied to periodic splines and to the Bernoulli monospline in § 6. The last § 7 states extensions of our results to bivariate cardinal splines. Previous chapter Next chapter RelatedDetails Published:1973ISBN:978-0-89871-009-0eISBN:978-1-61197-055-5 https://doi.org/10.1137/1.9781611970555Book Series Name:CBMS-NSF Regional Conference Series in Applied MathematicsBook Code:CB12Book Pages:vi + 119Key words:cardinal spline interpolation, spline functions, B-splines, exponential Euler splines, extremum and limit properties, Fourier transforms, histograms
Publication Year: 1973
Publication Date: 1973-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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Cited By Count: 628
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