By E. Arge, M. Dæhlen, T. Lyche, K. Mørken (auth.), J. C. Mason, M. G. Cox (eds.)
Read or Download Algorithms for Approximation II: Based on the proceedings of the Second International Conference on Algorithms for Approximation, held at Royal Military College of Science, Shrivenham, July 1988 PDF
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Additional info for Algorithms for Approximation II: Based on the proceedings of the Second International Conference on Algorithms for Approximation, held at Royal Military College of Science, Shrivenham, July 1988
The sequence of knots on the x-axis is then modified to 5. Numerical results In this section we use an example found in the literature, namely the test function F(x, y) = exp( _x 2 - y 2 ). The function is assumed specified by a sampie of values /; = Fi + (i, where U is the uniform distribution and the approximating spline is that of minimum norm. E. = where ei V'L. E. = 'L. leil/N S(Xi, Yi). 35 and MAX = l~i~N max leil, . ,. : " , '. ' .. ~ " ' . ' : . , . , ' p' . '. ~ .... :'... ~ :' ::. .....
Rank deficient matrices occur very frequently and lead to non-unique solutions. We can determine a particular solution selecting either the minimum norm solution (which, however, is not invariant under translation) or a geometrically invariant solution (Cox, 1986). 3. Knot placement From what we have said above, a need clearly arises for subdividing the rectangle R into a lattice that affords a good balance between the closeness of the fit to the data and the smoothness of the fit, whilst reducing the number of empty panels.
In The State oE the Art in Numerical Analysis, (Iserles, A. and Powell, M. J. ), Clarendon Press, Oxford, pp. 111-138. Dahmen, W. (1986), Sub division algorithms eonverge quadratieally. J. Comp. Appl. Math. 16, 145-158. Ferguson, D. , Frank, P. , and Jones, A. K. (1988), Surfaee shape eontrol using eonstrained optimization on the B-spline representation. CAGD 5, 87-103. Flet eher, R. (1987) Practical Methods oE Optimization, Seeond edition, John Wiley & Sons, Chi chester. Fontanella, F. (1987), Shape preserving surfaee interpolation.
Algorithms for Approximation II: Based on the proceedings of the Second International Conference on Algorithms for Approximation, held at Royal Military College of Science, Shrivenham, July 1988 by E. Arge, M. Dæhlen, T. Lyche, K. Mørken (auth.), J. C. Mason, M. G. Cox (eds.)