Spaces of generalized splines over T-meshes
We consider a class of non-polynomial spaces, namely a noteworthy case of Extended Chebyshev spaces, and we generalize the concept of polynomial spline space over T-mesh to this non-polynomial setting: in other words, we focus on a class of spaces spanned, in each cell of the T-mesh, both by polynom...
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| Published in: | Journal of computational and applied mathematics Vol. 294; pp. 102 - 123 |
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| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
01.03.2016
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| ISSN: | 0377-0427, 1879-1778 |
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| Abstract | We consider a class of non-polynomial spaces, namely a noteworthy case of Extended Chebyshev spaces, and we generalize the concept of polynomial spline space over T-mesh to this non-polynomial setting: in other words, we focus on a class of spaces spanned, in each cell of the T-mesh, both by polynomial and by suitably-chosen non-polynomial functions, which we will refer to as generalized splines over T-meshes. For such spaces, we provide, under certain conditions on the regularity of the space, a study of the dimension and of the basis, based on the notion of minimal determining set, as well as some results about the dimension of refined and merged T-meshes. Finally, we study the approximation power of the just constructed spline spaces. |
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| AbstractList | We consider a class of non-polynomial spaces, namely a noteworthy case of Extended Chebyshev spaces, and we generalize the concept of polynomial spline space over T-mesh to this non-polynomial setting: in other words, we focus on a class of spaces spanned, in each cell of the T-mesh, both by polynomial and by suitably-chosen non-polynomial functions, which we will refer to as generalized splines over T-meshes. For such spaces, we provide, under certain conditions on the regularity of the space, a study of the dimension and of the basis, based on the notion of minimal determining set, as well as some results about the dimension of refined and merged T-meshes. Finally, we study the approximation power of the just constructed spline spaces. |
| Author | Roman, Fabio Bracco, Cesare |
| Author_xml | – sequence: 1 givenname: Cesare surname: Bracco fullname: Bracco, Cesare email: cesare.bracco@unifi.it organization: Department of Mathematics and Computer Science “U. Dini”- University of Florence, V.le Morgagni 67/a, Florence 50134, Italy – sequence: 2 givenname: Fabio surname: Roman fullname: Roman, Fabio email: fabio.roman@unito.it organization: Department of Mathematics “G. Peano”- University of Turin, V. Carlo Alberto 10, Turin 10123, Italy |
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| SubjectTerms | Approximation Approximation power Basis functions Computation Construction Dimension formula Generalized splines Mathematical analysis Mathematical models Polynomials Regularity Splines T-mesh |
| Title | Spaces of generalized splines over T-meshes |
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