Lösung von Differentialgleichungen mit Splinefunktionen. Eine Störungstheorie. Tei 1: Divergenzaussagen.
Lösung von gewöhnlichen Differentialgleichungen mit nichtlinearen Splines.
Low rank Tucker-type tensor approximation to classical potentials
This paper investigates best rank-(r 1,..., r d) Tucker tensor approximation of higher-order tensors arising from the discretization of linear operators and functions in ℝd. Super-convergence of the best rank-(r 1,..., r d) Tucker-type decomposition with respect to the relative Frobenius norm is proven. Dimensionality reduction by the two-level Tucker-to-canonical approximation is discussed. Tensor-product representation of basic multi-linear algebra operations is considered, including inner, outer...
Low Volatility Options and Numerical Diffusion of Finite Difference Schemes
2000 Mathematics Subject Classification: 65M06, 65M12.In this paper we explore the numerical diffusion introduced by two nonstandard finite difference schemes applied to the Black-Scholes partial differential equation for pricing discontinuous payoff and low volatility options. Discontinuities in the initial conditions require applying nonstandard non-oscillating finite difference schemes such as the exponentially fitted finite difference schemes suggested by D. Duffy and the Crank-Nicolson variant...
Low-discrepancy point sets for non-uniform measures
We prove several results concerning the existence of low-discrepancy point sets with respect to an arbitrary non-uniform measure μ on the d-dimensional unit cube. We improve a theorem of Beck, by showing that for any d ≥ 1, N ≥ 1, and any non-negative, normalized Borel measure μ on there exists a point set whose star-discrepancy with respect to μ is of order . For the proof we use a theorem of Banaszczyk concerning the balancing of vectors, which implies an upper bound for the linear discrepancy...
Low-discrepancy point sets obtained by digital constructions over finite fields
Lower Bounds for the Condition Number of Vandermonde Matrices.
Lower Bounds for the Discrepancy of Triples of Inversive Congruential Pseudorandom Numbers with Power of Two Modulus.
Lower Bounds for the Zeros of Analytic Functions.
Lower Norm Estimates for Approximate Solutions of Differential Equations with Non-Smooth Coefficients.
Low-Mach consistency of a class of linearly implicit schemes for the compressible Euler equations
In this note, we give an overview of the authors’ paper [6] which deals with asymptotic consistency of a class of linearly implicit schemes for the compressible Euler equations. This class is based on a linearization of the nonlinear fluxes at a reference state and includes the scheme of Feistauer and Kučera [3] as well as the class of RS-IMEX schemes [8,5,1] as special cases. We prove that the linearization gives an asymptotically consistent solution in the low-Mach limit under the assumption of...
Low-rank iterative methods for projected generalized Lyapunov equations.
Low-rank tensor representation of Slater-type and Hydrogen-like orbitals
The paper focuses on a low-rank tensor structured representation of Slater-type and Hydrogen-like orbital basis functions that can be used in electronic structure calculations. Standard packages use the Gaussian-type basis functions which allow us to analytically evaluate the necessary integrals. Slater-type and Hydrogen-like orbital functions are physically more appropriate, but they are not analytically integrable. A numerical integration is too expensive when using the standard discretization...
Lp estimates of boundary integral equations for some nonlinear boundary value problems.
LU Decompositions of Generalized Diagonally Dominant Matrices