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  • Rychlost konvergence adaptivních waveletových metod závisí na podílu Rieszových konstant použitých waveletových bází. Cílem tohoto projektu je navrhnout konstrukci waveletových bází s co nejmenším podílem jejich Rieszových konstant a implementovat je v adaptivních waveletových metodách. (cs)
  • Wavelets are by now a widely accepted tool in signal and image processing as well as in numerical simulation. A function f that is smooth, except at some isolated singularities, typically has a sparse representation in a wavelet basis. This compression property of wavelets led to the design of adaptive wavelet methods for solving differential equations. The rate of convergence of these methods is strongly influenced by the choice of a wavelet basis, because the condition number of stiffness matrix representing discretized problem depends on a quotient of Riesz constants of a wavelet basis. The project will focus mainly on the following goals: 1) Construction of biorthogonal spline wavelet bases on the interval [0,1] with the quotient of their Riesz constants as small as possible. 2) Existence proof of the designed bases for arbitrary admissible degree for both primal and dual wavelets. 3) Adaptation of constructed wavelets on homogenous and complementary boundary conditions and expansion of constructed bases to more general domains. 4) Implementation of adaptive wavelet methods with new bases. (en)
Title
  • Wavelet adaptive methods with stable bases (en)
  • Waveletové adaptivní metody se stabilními bázemi (cs)
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  • biortogonální wavelety; adaptivní metody; Rieszovy konstanty; stabilní báze (en)
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