Multivariate Spline Functions and Their Applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Dordrecht
Springer Netherlands
2001
|
| Series: | Mathematics and Its Applications
529 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | As is known, the book named "Multivariate spline functions and their applications" has been published by the Science Press in 1994. This book is an English edition based on the original book mentioned 1 above with many changes, including that of the structure of a cubic-interpolation in n-dimensional spline spaces, and more detail on triangulations have been added in this book. Special cases of multivariate spline functions (such as step functions, polygonal functions, and piecewise polynomials) have been examined mathematically for a long time. I. J. Schoenberg (Contribution to the problem of application of equidistant data by analytic functions, Quart. Appl. Math., 4(1946), 45 - 99; 112 - 141) and W. Quade & L. Collatz (Zur Interpolations theories der reellen periodischen function, Press. Akad. Wiss. (PhysMath. KL), 30(1938), 383- 429) systematically established the theory of the spline functions. W. Quade & L. Collatz mainly discussed the periodic functions, while I. J. Schoenberg's work was systematic and complete. I. J. Schoenberg outlined three viewpoints for studing univariate splines: Fourier transformations, truncated polynomials and Taylor expansions. Based on the first two viewpoints, I. J. Schoenberg deduced the B-spline function and its basic properties, especially the basis functions. Based on the latter viewpoint, he represented the spline functions in terms of truncated polynomials. These viewpoints and methods had significantly effected on the development of the spline functions |
| Physical Description: | 1 Online-Ressource (XII, 512 p) |
| ISBN: | 9789401723787 9789048157037 |
| DOI: | 10.1007/978-94-017-2378-7 |
Staff View
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| 500 | |a As is known, the book named "Multivariate spline functions and their applications" has been published by the Science Press in 1994. This book is an English edition based on the original book mentioned 1 above with many changes, including that of the structure of a cubic-interpolation in n-dimensional spline spaces, and more detail on triangulations have been added in this book. Special cases of multivariate spline functions (such as step functions, polygonal functions, and piecewise polynomials) have been examined mathematically for a long time. I. J. Schoenberg (Contribution to the problem of application of equidistant data by analytic functions, Quart. Appl. Math., 4(1946), 45 - 99; 112 - 141) and W. Quade & L. Collatz (Zur Interpolations theories der reellen periodischen function, Press. Akad. Wiss. (PhysMath. KL), 30(1938), 383- 429) systematically established the theory of the spline functions. W. Quade & L. Collatz mainly discussed the periodic functions, while I. J. Schoenberg's work was systematic and complete. I. J. Schoenberg outlined three viewpoints for studing univariate splines: Fourier transformations, truncated polynomials and Taylor expansions. Based on the first two viewpoints, I. J. Schoenberg deduced the B-spline function and its basic properties, especially the basis functions. Based on the latter viewpoint, he represented the spline functions in terms of truncated polynomials. These viewpoints and methods had significantly effected on the development of the spline functions | ||
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:15Z |
| institution | BVB |
| isbn | 9789401723787 9789048157037 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859703 |
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| publisher | Springer Netherlands |
| record_format | marc |
| series | Mathematics and Its Applications |
| series2 | Mathematics and Its Applications |
| spelling | Wang, Ren-Hong 1937- Verfasser (DE-588)1014568838 aut Multivariate Spline Functions and Their Applications by Ren-Hong Wang Dordrecht Springer Netherlands 2001 1 Online-Ressource (XII, 512 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 529 As is known, the book named "Multivariate spline functions and their applications" has been published by the Science Press in 1994. This book is an English edition based on the original book mentioned 1 above with many changes, including that of the structure of a cubic-interpolation in n-dimensional spline spaces, and more detail on triangulations have been added in this book. Special cases of multivariate spline functions (such as step functions, polygonal functions, and piecewise polynomials) have been examined mathematically for a long time. I. J. Schoenberg (Contribution to the problem of application of equidistant data by analytic functions, Quart. Appl. Math., 4(1946), 45 - 99; 112 - 141) and W. Quade & L. Collatz (Zur Interpolations theories der reellen periodischen function, Press. Akad. Wiss. (PhysMath. KL), 30(1938), 383- 429) systematically established the theory of the spline functions. W. Quade & L. Collatz mainly discussed the periodic functions, while I. J. Schoenberg's work was systematic and complete. I. J. Schoenberg outlined three viewpoints for studing univariate splines: Fourier transformations, truncated polynomials and Taylor expansions. Based on the first two viewpoints, I. J. Schoenberg deduced the B-spline function and its basic properties, especially the basis functions. Based on the latter viewpoint, he represented the spline functions in terms of truncated polynomials. These viewpoints and methods had significantly effected on the development of the spline functions Mathematics Electronic data processing Computer vision Computer science / Mathematics Engineering design Approximations and Expansions Computational Mathematics and Numerical Analysis Numeric Computing Image Processing and Computer Vision Engineering Design Datenverarbeitung Informatik Mathematik Spline-Funktion (DE-588)4056332-7 gnd rswk-swf Mehrere Variable (DE-588)4277015-4 gnd rswk-swf Spline-Funktion (DE-588)4056332-7 s Mehrere Variable (DE-588)4277015-4 s 1\p DE-604 Mathematics and Its Applications 529 (DE-604)BV008163334 529 https://doi.org/10.1007/978-94-017-2378-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Wang, Ren-Hong 1937- Multivariate Spline Functions and Their Applications Mathematics and Its Applications Mathematics Electronic data processing Computer vision Computer science / Mathematics Engineering design Approximations and Expansions Computational Mathematics and Numerical Analysis Numeric Computing Image Processing and Computer Vision Engineering Design Datenverarbeitung Informatik Mathematik Spline-Funktion (DE-588)4056332-7 gnd Mehrere Variable (DE-588)4277015-4 gnd |
| subject_GND | (DE-588)4056332-7 (DE-588)4277015-4 |
| title | Multivariate Spline Functions and Their Applications |
| title_auth | Multivariate Spline Functions and Their Applications |
| title_exact_search | Multivariate Spline Functions and Their Applications |
| title_full | Multivariate Spline Functions and Their Applications by Ren-Hong Wang |
| title_fullStr | Multivariate Spline Functions and Their Applications by Ren-Hong Wang |
| title_full_unstemmed | Multivariate Spline Functions and Their Applications by Ren-Hong Wang |
| title_short | Multivariate Spline Functions and Their Applications |
| title_sort | multivariate spline functions and their applications |
| topic | Mathematics Electronic data processing Computer vision Computer science / Mathematics Engineering design Approximations and Expansions Computational Mathematics and Numerical Analysis Numeric Computing Image Processing and Computer Vision Engineering Design Datenverarbeitung Informatik Mathematik Spline-Funktion (DE-588)4056332-7 gnd Mehrere Variable (DE-588)4277015-4 gnd |
| topic_facet | Mathematics Electronic data processing Computer vision Computer science / Mathematics Engineering design Approximations and Expansions Computational Mathematics and Numerical Analysis Numeric Computing Image Processing and Computer Vision Engineering Design Datenverarbeitung Informatik Mathematik Spline-Funktion Mehrere Variable |
| url | https://doi.org/10.1007/978-94-017-2378-7 |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT wangrenhong multivariatesplinefunctionsandtheirapplications |