Four-point Transformation Methods in Approximation and the Smoothing Problems
نویسنده
چکیده
The main goal of the adaptive local strategy consists in reducing the complexity of computational problems. We propose a new approach to curve approximation and smoothing based on 4-point transformations or Discrete Projective Transforms (DPT). In the framework of DPT the variable point is related to three data points (accompanying points). The variable y ordinate is expressed via the convolution of accompanying y ordinates and weight functions that are deˇned as cross-ratio functions of four x coordinates. DPT has some attractive properties (natural norming, scale invariance, threefold symmetry, ®4-point ̄ orthogonality), which are useful in designing new algorithms. Diverse methods and algorithms based on DPT have been developed.
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