Asymptotic behaviour of fixed-order error constants of modified quadrature formulae for Cauchy principal value integrals.
Asymptotic Minimum Norm Quadrature Formulae.
Asymptotic optimality of generalized cross-validation for choosing the regularization parameter.
Attenuation Factors in Multivariate Fourier Analysis.
Automatic differentiation and its program realization
Automatic differentiation is an effective method for evaluating derivatives of function, which is defined by a formula or a program. Program for evaluating of value of function is by automatic differentiation modified to program, which also evaluates values of derivatives. Computed values are exact up to computer precision and their evaluation is very quick. In this article, we describe a program realization of automatic differentiation. This implementation is prepared in the system UFO, but its...
Automatic differentiation platform : design
Automatic differentiation (AD) has proven its interest in many fields of applied mathematics, but it is still not widely used. Furthermore, existing numerical methods have been developed under the hypotheses that computing program derivatives is not affordable for real size problems. Exact derivatives have therefore been avoided, or replaced by approximations computed by divided differences. The hypotheses is no longer true due to the maturity of AD added to the quick evolution of machine capacity....
Automatic Differentiation Platform: Design
Automatic differentiation (AD) has proven its interest in many fields of applied mathematics, but it is still not widely used. Furthermore, existing numerical methods have been developed under the hypotheses that computing program derivatives is not affordable for real size problems. Exact derivatives have therefore been avoided, or replaced by approximations computed by divided differences. The hypotheses is no longer true due to the maturity of AD added to the quick evolution of machine capacity....
Autoregressive error-processes, cubic splines and tridiagonal matrices
In the paper formulate for the inversion of some tridiagonal matrices are given. The results can be applied to the autoregressive processes.
Averaging of gradient in the space of linear triangular and bilinear rectangular finite elements
An averaging method for the second-order approximation of the values of the gradient of an arbitrary smooth function u = u(x 1, x 2) at the vertices of a regular triangulation T h composed both of rectangles and triangles is presented. The method assumes that only the interpolant Πh[u] of u in the finite element space of the linear triangular and bilinear rectangular finite elements from T h is known. A complete analysis of this method is an extension of the complete analysis concerning the finite...
Avoiding look-ahead in the Lanczos method and Padé approximation
In the non-normal case, it is possible to use various look-ahead strategies for computing the elements of a family of regular orthogonal polynomials. These strategies consist in jumping over non-existing and singular orthogonal polynomials by solving triangular linear systems. We show how to avoid them by using a new method called ALA (Avoiding Look-Ahead), for which we give three principal implementations. The application of ALA to Padé approximation, extrapolation methods and Lanczos method for...
-spline representation of interpolating and smoothing quadratic spline
Backward Error Analysis for Totally Positive Linear Systems.
Barycentric Formulae for Cardinal (SINC-) Interpolants.
Bases de type Schauder de C [0,1] et formules de quadrature associées.
Basic relations valid for the Bernstein spaces and their extensions to larger function spaces via a unified distance concept
Some basic theorems and formulae (equations and inequalities) of several areas of mathematics that hold in Bernstein spaces are no longer valid in larger spaces. However, when a function f is in some sense close to a Bernstein space, then the corresponding relation holds with a remainder or error term. This paper presents a new, unified approach to these errors in terms of the distance of f from . The difficult situation of derivative-free error estimates is also covered.
Bessel Transforms and Rational Extrapolation.
Best Constants Occuring with the Modulus of Continuity in the Error Estimate for Spline Interpolants of Odd Degree on Equidistant Grids.
Best quadrature formula for a certain class of analytic functions
Beweis einiger Sätze über die analytische Ausgleichung. I
Beweis einiger Sätze über die analytische Ausgleichung. II