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| ON STABILITY OF m-VARIATE C~1 INTERPOLATION | |
| 作者姓名： | J.Peters M.Sitharam |
| 作者单位： | Department of Mathematics Rensselaer Polytechnic Institute Troy NY 12180-3590 U.S.A.，Mathematical Sciences Kent State University Kent OH 44242 U.S.A. |
| 摘 要： | A.simplicial mesh(triangulation)is constructed that generalizes the two-dimensional 4-directionmesh to R~m.This mesh,with symmetric,shift-invariant values at the vertices,is shown to admit a boundedC~1 interpolant if and only if the alternating sum of the values at the vertices of any 1-cube is zero.This im-plies thai interpolation at the vertices of an m-dimensional,simplicial mesh by a C~1 piecewise polynomial ofdegree m+1 with one piece per simplex is unstable. |
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