We introduce a WENO reconstruction based on Hermite interpolation both for semi-Lagrangian and finite difference methods. This WENO reconstruction technique allows to control spurious oscillations. We develop third and fifth order methods and apply them to non-conservative semi-Lagrangian schemes and conservative finite difference methods. Our numerical results will be compared to the usual sem...

Several optimal eighth order methods to obtain simple roots are analyzed. The methods are based on two step, fourth order optimal methods and a third step of modified Newton. The modification is performed by taking an interpolating polynomial to replace either f ðznÞ or f ðznÞ. In six of the eight methods we have used a Hermite interpolating polynomial. The other two schemes use inverse interpo...

In this paper, we give explicit construction of multiwavelets on polygonal region in R 2 that is associated with a nested triangular tessellation. Two di erent constructions will be presented. The rst construction is very similar to Alpert's construction in [3], but unlike the latter 1-D construction, in which case symmetry of basis functions comes in almost automatically, the multiwavelets fro...

A biorthogonal formulation is applied to the non-Hermite transcorrelated Hamiltonian, which treats a large amount of the dynamic correlation effects implicitly. We introduce biorthogonal canonical orbitals diagonalizing the non-Hermitian Fock operator. We also formulate many-body perturbation theory for the transcorrelated Hamiltonian. The biorthogonal self-consistent field followed by the seco...

By applying finite difference formula to time discretization and the cubic B-splines for spatial variable, a numerical method for solving the inverse system of Burgers equations is presented. Also, the convergence analysis and stability for this problem are investigated and the order of convergence is obtained. By using two test problems, the accuracy of presented method is verified. Additional...

The biorthogonal wavelets introduced by Cohen, Daubechies, and Feauveau contain in particular compactly supported biorthogonal spline wavelets with compactly supported duals. We present a new approach for the construction of compactly supported spline wavelets, which is entirely based on properties of splines in the time domain. We are able to characterize a large class of such wavelets which c...

The ubiquitous problem of estimating the background of a measured spectrum is solved with Bayesian probability theory. A mixture model is used to capture the defining characteristics of the problem, namely that the background is smoother than the signal. The smoothness property is quantified in terms of a cubic spline basis where a variable degree of smoothness is attained by allowing the numbe...

(Bi)orthogonal (multi)wavelets on the real line have been extensively studied and employed in applications with success. A lot of problems are defined bounded intervals or domains. Therefore, it is important both theory application to construct all possible wavelets some desired properties from (bi)orthogonal line. Vanishing moments compactly supported key property for sparse wavelet representa...

We present a novel method for determining local multiresolution filters for B-spline subdivision curves of any order. Our approach is based on constraining the wavelet coefficients such that the coefficients at even vertices can be computed from the coefficients of neighboring odd vertices. This constraint leads to an initial set of decomposition filters. To increase the quality of these initia...