## 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 1988This volume comprises the proceedings of the second Shrivenham conference on Algorithms for Approximation. The term 'approximation' here refers to 'the approximation of functions and data by similar functions', and leads to such topics as curve and surface fitting, spline and piecewise polynomial methods, finite element modelling, and computer-aided design. Applications are given to a wide variety of areas such as surveying, meteorology, radar antenna and acoustic array design, topography, engineering metrology, and CAD/CAM. Emphasis at the meeting was placed on the development of useful algorithms, and on practical applications in defence and industry.In addition, some 40 submitted papers were selected and presented on a multitude of topics such as multivariate interpolation, optimization methods, constrained problems, spline fitting, data modelling, and applications in microwave measurement, isotropic antennas, sound measurement, and digitized contours. |

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### Contents

Constrained spline approximation of functions and | 4 |

E Arge M Dahlen T Lyche and K Morken | 21 |

G T Anthonyt and M G | 30 |

Copyright | |

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applied approximation problem Approximation Theory asymptotic B-splines calculations cardinal function Chebyshev approximation Chebyshev polynomials coefficients computation conjugate gradient consider constraints construction convex corresponding cost function cubic spline curve Dahmen data dependent triangulations data fitting data points data set defined denotes derivative determined differential discrete edge eigenvalues elements error estimate example Figure finite formula Fourier geometric given grid initial integral inverse iteration knot placement knot vector Lemma linear programming M. G. Cox Math Mathematics matrix method Mi-sphere Micchelli minimize multiquadric multivariate Multivariate interpolation National Physical Laboratory noisy data nonlinear norm obtained optimal orthogonal penalized least squares polynomial of degree Proof properties quadratic quadrature radial basis function Remez algorithm residual satisfies scheme sequence SIAM solving space sphere spline functions Step strategy subdivision subset surface swapping symmetric system of equations Theorem thin plate spline values variables Wahba zero