## Algorithms for Approximation: 2This 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 Dwhlen T Lyche and K Morken | 21 |

An algorithm for knot location in bivariate least | 30 |

Copyright | |

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analysis application approximation problem Approximation Theory asymptotic B-spline Barrodale cardinal function Chebyshev Chebyshev approximation Chebyshev polynomials coefficients complex computation conjugate gradient consider constraints construction convergence convex corresponding cubic spline curve Dahmen data dependent triangulations data points data set defined denotes derivative differential discrete edge eigenvalues elements error estimate example Figure finite ﬁrst ﬁt ﬁtting formula Fourier geometric given grid initial inverse iteration knot placement knot vector L1 norm L1 solution Lemma linear programming Math Mathematics matrix method Micchelli minimize multiquadric multivariate Multivariate interpolation National Physical Laboratory noisy data nonlinear nulls obtained optimal orthogonal parameters penalized least squares phase piecewise polynomial approximation Proof properties quadratic radial basis function Remez algorithm residual satisfy sequence SIAM smoothing solving space sphere step strategy subset surface swapping symmetric system of equations Theorem thin plate spline values variables Wahba zero