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By B. Weisfeiler

ISBN-10: 3540080511

ISBN-13: 9783540080510

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Example text

A¢ ,x . c > 0, for all X and c E JRN \ {O} with pl · c = O. 8), on th e order m of t he polynom ial space P '/;" . 12) is empty, in which case is, according to Definition 8, positi ve definite . This altogether leads us to t he following definiti on. 36 3 Radial Basis Functions Definition 9. 12) holds for all possible choices of finite point sets Xc IRd . 1. Note that for any pair ml, m2 E No with ml ::; m2, we have the inclusion CPDd(md c CPD d(m2) . 12) is the order of ¢. Note that PDd = CPD(O), and so the order of any positive definite ¢ E PD d, is zero.

18 2 Algorithms and Data Structures Nearly C 1 Criteria (NCl) . For a vari ety of different test cases it is shown in [58, 59, 60] th at data-dependent triangulations, which ar e producing long and thin triangles can significantly improve the approximation quality of the resulting piecewise linear interpol ation. , f has large second-order directional derivatives in one dir ection, compa red with other dir ections. In this case, the long side of the trian gles should point into the directions of small cur vat ure .

Theorem 4. 15). In this case, m = fso/21 is the order of

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On Construction and Identification of Graphs by B. Weisfeiler

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