Abstract
We present an adaptive method to extract shape-preserving information from a univariate data sample. The behavior of the signal is obtained by interpolating at adaptively selected few data points by a linear combination of multiquadrics with variable scaling parameters. On the theoretical side, we give a sufficient condition for existence of the scaled multiquadric interpolant. On the practical side, we give various examples to show the applicability of the method.
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References
R.E. Hagan and E.J. Kansa, Studies of the r parameter in the multiquadric function applied to ground water pumping, J. Appl. Sci. Comput. 1 (1994) 266–281.
R.L. Hardy, Multiquadric equations of topography and other irregular surfaces, J. Geophys. Res. 76 (1971) 1905–1915.
W.L. Hwang and S. Mallat, Singularity detection and processing with wavelets, IEEE Trans. Inform. Theory 38 (1992) 617–643.
T. Lyche and K. Morken, A data reduction strategy for splines with applications to the approximation of functions and data, IMA J. Numer. Anal. 8 (1988) 185–208.
S. Mallat and S. Zhong, Characterization of signals from multiscale edges, IEEE Trans. Pattern Anal. Mach. Intell. 14 (1992) 710–732.
S. Rippa, An algorithm for selecting a good value for the parameter c, Adv. Comput. Math. 11 (1999) 193–210.
L. Schumaker and S. Stanley, Shape-preserving knot removal, Comput. Aided Geom. Design 13 (1996) 851–872.
Z. Wu and R. Schaback, Shape preserving properties and convergence of univariate multiquadric quasi-interpolation, Acta Math. Appl. Sin. Engl. Ser. 10(4) (1994) 441–446.
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Bozzini, M., Lenarduzzi, L. & Schaback, R. Adaptive Interpolation by Scaled Multiquadrics. Advances in Computational Mathematics 16, 375–387 (2002). https://doi.org/10.1023/A:1014584220418
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DOI: https://doi.org/10.1023/A:1014584220418