Abstract
In 2000, W. Dahmen et al. proposed a construction of Hermite cubic spline multi-wavelets adapted to the interval [0, 1]. Later, several more simple constructions of wavelet bases based on Hermite cubic splines were proposed. We focus here on wavelet basis with respect to which both the mass and stiffness matrices are sparse in the sense that the number of non-zero elements in each column is bounded by a constant. Then, a matrix-vector multiplication in adaptive wavelet methods can be performed exactly with linear complexity for any second order differential equation with constant coefficients. In this contribution, we shortly review these constructions, use an anisotropic tensor product to obtain bases on the cube [0, 1]3, and compare their condition numbers.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
