Sparse Wavelet Representation of Differential Operators with Piecewise Polynomial Coefﬁcients

dc.contributor.author	Černá, Dana
dc.contributor.author	Finěk, Václav
dc.date.accessioned	2019-07-25T09:03:01Z
dc.date.available	2019-07-25T09:03:01Z
dc.date.issued	2019-02-22
dc.description.abstract	We propose a construction of a Hermite cubic spline-wavelet basis on the interval and hypercube. The basis is adapted to homogeneous Dirichlet boundary conditions. The wavelets are orthogonal to piecewise polynomials of degree at most seven on a uniform grid. Therefore, the wavelets have eight vanishing moments, and the matrices arising from discretization of differential equations with coefficients that are piecewise polynomials of degree at most four on uniform grids are sparse. Numerical examples demonstrate the efficiency of an adaptive wavelet method with the constructed wavelet basis for solving the one-dimensional elliptic equation and the two-dimensional Black–Scholes equation with a quadratic volatility.	cs
dc.format.extent	21 stran	cs
dc.identifier.doi	10.3390/axioms6010004
dc.identifier.uri	https://dspace.tul.cz/handle/15240/152966
dc.identifier.uri	https://www.mdpi.com/2075-1680/6/1/4
dc.language.iso	cs	cs
dc.publisher	MDPI
dc.relation.ispartof	Axioms
dc.subject	Riesz basis	cs
dc.subject	wavelet	cs
dc.subject	spline	cs
dc.subject	interval	cs
dc.subject	differential equation	cs
dc.subject	sparse matrix	cs
dc.subject	Black–Scholes equation	cs
dc.title	Sparse Wavelet Representation of Differential Operators with Piecewise Polynomial Coefﬁcients	cs
local.relation.issue	1
local.relation.volume	6

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