On construction of bivariate and trivariate vertex splines on arbitrary mixed grid partitions /
| Main Author: | |
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| Other Authors: | , , |
| Format: | Thesis Book |
| Language: | English |
| Published: |
1989.
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| Subjects: | |
| Online Access: | Link to OAKTrust copy |
| Abstract: | The procedures for constructing vertex splines in various spline spaces [see PDF for symbol] in the bivariate and trivariate settings are described and approximation formulas based on these vertex splines are constructed in this thesis. These vertex splines span a super spline subspace of [see PDF for symbol] and the optimal approximation order of [see PDF for symbol] is attained by using these approximation formulas. Here, [see PDF for symbol] stands for the following space of all piecewise polynomial functions of degree d and of smoothness order r on a given grid partition Δ: (i) r (greater than or equal to sign) 1, d (greater than or equal to sign) 3r + 2, and Δ consists of triangles and parallelograms in the bivariate setting; (ii) r=1, d=7, and Δ consists of tetrahedral and satisfies that the number of tetrahedra around each nonsingular edge is odd in the trivariate setting; (iii) r (greater than or equal to sign) 1, d (greater than or equal to sign) 6r + 3, and Δ consists of tetrahedra in the trivariate setting; and (iv) r (greater than or equal to sign) 1, d (greater than or equal to sign) 8r + 1, and Δ consists of tetrahedra, prisms and parallelepipeds in the trivariate setting. |
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| Item Description: | Typescript (photocopy). Vita. "Major subject: Mathematics." |
| Physical Description: | viii, 139 leaves : illustrations ; 29 cm |
| Bibliography: | Includes bibliographical references. |