A new proof of some inequality connected with quadratures.
A new source of structured singular value decomposition problems.
A nodal spline interpolant for the Gregory rule of even order.
A note on direct methods for approximations of sparse Hessian matrices
Necessity of computing large sparse Hessian matrices gave birth to many methods for their effective approximation by differences of gradients. We adopt the so-called direct methods for this problem that we faced when developing programs for nonlinear optimization. A new approach used in the frame of symmetric sequential coloring is described. Numerical results illustrate the differences between this method and the popular Powell-Toint method.
A note on finite quadrature rules with a kind of Freud weight function.
A note on linear approximations of matrices
A note on Newbery's algorithm for discrete least-squares approximation by trigonometric polynomials.
A Note on Polynomial Splines with Free Knots.
A note on the perturbed trapezoid inequality.
A note on the rate of convergence for Chebyshev-Lobatto and Radau systems
This paper is devoted to Hermite interpolation with Chebyshev-Lobatto and Chebyshev-Radau nodal points. The aim of this piece of work is to establish the rate of convergence for some types of smooth functions. Although the rate of convergence is similar to that of Lagrange interpolation, taking into account the asymptotic constants that we obtain, the use of this method is justified and it is very suitable when we dispose of the appropriate information.
A numerical method for solution of semidifferential equations
A numerical method of fitting a multiparameter nonlinear function to experimental data in the norm
A numerical method of fitting a multiparameter function, non-linear in the parameters which are to be estimated, to the experimental data in the norm (i.e., by minimizing the sum of absolute values of errors of the experimental data) has been developed. This method starts with the least squares solution for the function and then minimizes the expression , where is the error of the -th experimental datum, starting with an comparable with the root-mean-square error of the least squares solution...
A numerical sampling problem and the Weyl pseudorandom numbers.
A Numerical study of Newton interpolation with extremely high degrees
In current textbooks the use of Chebyshev nodes with Newton interpolation is advocated as the most efficient numerical interpolation method in terms of approximation accuracy and computational effort. However, we show numerically that the approximation quality obtained by Newton interpolation with Fast Leja (FL) points is competitive to the use of Chebyshev nodes, even for extremely high degree interpolation. This is an experimental account of the analytic result that the limit distribution of FL...
A Nyström method for boundary integral equations in domains with corners.
A parallel algorithm for discrete least squares rational approximation.
A particular smooth interpolation that generates splines
There are two grounds the spline theory stems from - the algebraic one (where splines are understood as piecewise smooth functions satisfying some continuity conditions) and the variational one (where splines are obtained via minimization of some quadratic functionals with constraints). We use the general variational approach called smooth interpolation introduced by Talmi and Gilat and show that it covers not only the cubic spline and its 2D and 3D analogues but also the well known tension spline...
A priori error estimates for Lagrange interpolation on triangles
We present the error analysis of Lagrange interpolation on triangles. A new a priori error estimate is derived in which the bound is expressed in terms of the diameter and circumradius of a triangle. No geometric conditions on triangles are imposed in order to get this type of error estimates. To derive the new error estimate, we make use of the two key observations. The first is that squeezing a right isosceles triangle perpendicularly does not reduce the approximation property of Lagrange interpolation....
A Probabilistic Theory for Error Estimation in Automatic Integration.
A property of divided differences with multiple nodes.