Abstract In this paper, we present a new simple method for solving two integral equations of Love’s type that have many applications, especially in electrostatic systems. The approach the solution is based on an innovative technique using matrix algebra barycentric Lagrange interpolation. unknown function expressed through product four matrices. kernel interpolated twice, so get it five Additio...

We review recently developed methods of constructing Lagrange and Her-mite interpolation sets for bivariate splines on triangulations of general type. Approximation order and numerical performance of our methods are also discussed.

Using the concept of Geometric Weakly Admissible Meshes (see §2 below) together with an algorithm based on the classical QR factorization of matrices, we compute efficient points for discrete multivariate least squares approximation and Lagrange interpolation.

The paper deals with the Lagrange interpolation of functions having a bounded variation derivative. For special systems of nodes, it is shown that this polynomial sequence converges with the best approximation order. The L weighted case is also discussed.

We present a stable and convergent method for solving initial value problems based on the use of differentiation matrices obtained by Lagrange interpolation. This implicit multistep-like method is easy-to-use and performs pretty well in the solution of mildly stiff problems and it can also be applied directly to differential problems in the complex plane.

In this paper properties of cell matrices are studied. A determinant of such a matrix is given in a closed form. In the proof a general method for determining a determinant of a symbolic matrix with polynomial entries, based on multivariate polynomial Lagrange interpolation, is outlined. It is shown that a cell matrix of size n > 1 has exactly one positive eigenvalue. Using this result it is pr...

In the paper, the Lagrange geometric interpolation by spatial rational cubic Bézier curves is studied. It is shown that under some natural conditions the solution of the interpolation problem exists and is unique. Furthermore, it is given in a simple closed form which makes it attractive for practical applications. Asymptotic analysis confirms the expected approximation order, i.e., order six. ...

We obtain converse Marcinkiewicz-Zygmund inequalities such as k P kLp[ 1;1] C 0@ n X j=1 j jP (tj)j 1A1=p for polynomials P of degree n 1, under general conditions on the points ftjgj=1 and on the function . The weights f jgj=1 are appropriately chosen. We illustrate the results by applying them to extended Lagrange interpolation for exponential weights on [ 1; 1].

Budapest In this note I will mainly discuss the joint work of Turán and mvself and some of my own results and I do not claim to give a survey of the whole subject. Let-1 c xl <. .. < xn < 1 be n points in (-1, +1). Denote bv_ l k (x) the fundamental functions of Lagrange interpolation, we have n 1, (x) = 0(x)-w(x) = L((x-xk). ~~'(xk)(x-xk~ k=1 n It is well known that the sum 1lk (x) I plays a f...