By E. Arge, M. Dæhlen, T. Lyche, K. Mørken (auth.), J. C. Mason, M. G. Cox (eds.)

ISBN-10: 0412345803

ISBN-13: 9780412345807

ISBN-10: 1489934421

ISBN-13: 9781489934420

**Read Online 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 resources 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**

**Example text**

E. E. E. 8577 E - 03 MAX 02 N 6. 3078E - 03 Concluding re marks For small data sets, the algorithm presented provides good results both for data on a mesh and for scattered data. For large data sets, our results compare favourably with those provided by methods discussed in the literature. The comparison holds also for computation time. Moreover, memory requirements are not excessive, so the algorithm can be used on a personal computer and can be modified for interactive use.

When defining the linear space of splines from which the fit is to be taken, there is considerable freedom of choice in both the order n of the spline and in the number and locations ofthe interior knots Aj, j = 1, ... , N. We are interested in constructing strategies and algorithms for automatically choosing A = (All"" AN) so that the spline fit of given order with these knots is, in some sense, an "acceptable" fit to the data. 37 In Cox, Harris and Jones (1987) we discuss various approaches to solving the problem of automatie knot placement.

0. '0 O'OS! '00 '00 200 '00 '00 SOll "'" 100 '00 >00 '00 '00 SOll "'" 100 ... 35 CI. I" 0. '. O. OS ~ _'00 BOO 0()() FIG. 3. S. 00280). s. 00295). s. 73 x 10- 7 ). 43 This arises from very accurate measurements of the response of a photodiode. The data set consists of 1024 points with equispaced xi-values. For clarity, we have plotted only every fifth point in the diagrams of Figure 3. A set of 79 knots is initially generated and this is reduced to 55 when clusters are removed as described above.

### 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.)

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