Parsian, H. Two-dimensional Legendre wavelets and operational matrices of integration. (English) Zbl 1092.65021 Acta Math. Acad. Paedagog. Nyházi. (N.S.) 21, 101-106 (2005). Summary: One-dimensional Legendre wavelets are the basis of a numerical method for solving one-dimensional variational problems and integral equations. In this paper we introduce two-dimensional Legendre wavelets. These wavelets are defined over the interval \([0,1]\times[0,1]\) and an orthonormal set over this interval. The integration of the product of two-dimensional Legendre wavelets over \([0,1]\times[0,1]\) is equal one. We compute operational matrices of integration for two-dimensional Legendre wavelets. These operational matrices are suitable tools for two-dimensional problems. Two-dimensional Legendre wavelets are a numerical method for solving two-dimensional variational problems. Cited in 5 Documents MSC: 65D32 Numerical quadrature and cubature formulas 65T60 Numerical methods for wavelets 42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems Keywords:Legendre wavelets; numerical integration; orthogonal set PDFBibTeX XMLCite \textit{H. Parsian}, Acta Math. Acad. Paedagog. Nyházi. (N.S.) 21, 101--106 (2005; Zbl 1092.65021) Full Text: EuDML EMIS