Related papers: Numerical integration rules based on B-spline base…
We propose a method to efficiently compute tomographic projections of a 3D volume represented by a linear combination of shifted B-splines. To do so, we propose a ray-tracing algorithm that computes 3D line integrals with arbitrary…
Recently the author and U. Reif introduced the concept of diversification of uniform tensor product B-splines. Based on this concept, we give a new constructive modification of non-uniform B-splines. The resulting spline spaces are…
One of the main purposes of this article is to give functional equations and differential equations between Bernstein basis functions and generating functions of B-spline curves. Using these equations, very useful formulas containing the…
Simulations of biophysical systems inevitably include steps that correspond to time integrations of ordinary differential equations. These equations are often related to enzyme action in the synthesis and destruction of molecular species,…
In this paper we investigate numerically the order of convergence of an isogeometric collocation method that builds upon the least-squares collocation method presented in [1] and the variational collocation method presented in [2]. The…
This survey gives an overview of several fundamental algebraic constructions which arise in the study of splines. Splines play a key role in approximation theory, geometric modeling, and numerical analysis, their properties depend on…
Functions on a bounded domain in scientific computing are often approximated using piecewise polynomial approximations on meshes that adapt to the shape of the geometry. We study the problem of function approximation using splines on a…
This paper presents high-order numerical methods for solving boundary value problems associated with the Lane-Emden equation, which frequently arises in astrophysics and various nonlinear models. A major challenge in studying this equation…
This contribution investigates the connection between isogeometric analysis and integral equation methods for full-wave electromagnetic problems up to the low-frequency limit. The proposed spline-based integral equation method allows for an…
In this paper, we introduce a type of tensor neural network. For the first time, we propose its numerical integration scheme and prove the computational complexity to be the polynomial scale of the dimension. Based on the tensor product…
Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of…
The object of the present paper is to extend the third-order iterative method for solving nonlinear equations into systems of nonlinear equations. Since our motive is to develop the method which improve the order of convergence of Newton's…
In the random case setting, scrambled polynomial lattice rules as discussed in \cite{BD10} enjoy more favourable strong tractablility properties than scrambled digital nets. This short note discusses the application of scrambled polynomial…
We describe some new univariate spline quasi-interpolants on uniform partitions of bounded intervals. Then we give some applications to numerical analysis: integration, differentiation and approximation of zeros.
Trigonometric and hyperbolic B-splines can be computed via recurrence relations analogous to the classical polynomial B-splines. However, in their original formulation, these two types of B-splines do not form a partition of unity and…
In this study, we introduce a refined method for ascertaining error estimations in numerical simulations of dynamical systems via an innovative application of composition techniques. Our approach involves a dual application of a basic…
Approximating a definite integral of product of cosines to within an accuracy of n binary digits where the integrand depends on input integers x[k] given in binary radix, is equivalent to counting the number of equal-sum partitions of the…
This manuscript presents a novel and reliable third-order iterative procedure for computing the zeros of solutions to second-order ordinary differential equations. By approximating the solution of the related Riccati differential equation…
The numerical integration method has been routinely used to produce global standard gravitational models from satellite tracking measurements of CHAMP/GRACE types. It is implemented by solving the differential equations of the partial…
Using elementary methods, we define and derive a particular weighted average of the trapezoidal and composite trapezoidal rules and show that this approximation, as well as its composite, is straightforward in computation. This…