Optimization problems over several cones of non-negative polynomials are described; we focus on linear constraints on the coefficients that represent interpolation constraints. For these problems, the complexity of solving the dual formulation is shown to be almost independent of the number of constraints, provided that an appropriate preprocessing has been performed. These results are also ext...

Abstract. We construct a new adaptive algorithm for radial basis functions (RBFs) method applied to interpolation, boundary-value, and initialboundary-value problems with localized features. Nodes can be added and removed based on residuals evaluated at a finer point set. We also adapt the shape parameters of RBFs based on the node spacings to prevent the growth of the conditioning of the inter...

We present a numerically fast reduced filtering strategy, the Fourier domain Kalman filter with appropriate interpolations to account for irregularly spaced observations of complex turbulent signals. The design of such a reduced filter involves: (i) interpolating irregularly spaced observations to the model regularly spaced grid points, (ii) understanding under which situation the small scale o...

is positive semidefinite for every choice of an integer n and of n points z1, . . . , zn ∈ D. The significance of this characterization for interpolation theory is that it gives the necessity part in the Nevanlinna-Pick interpolation theorem: given points z1, . . . , zn ∈ D and w1, . . . , wn ∈ C, there exists w ∈ S with w(zj) = wj for j = 1, . . . , n if and only if the associated Pick matrix ...

In this paper a new element for analysis of thin-walled structures is presented, and the effects of secondary shear stresses on longitudinal displacements are examined. Since the Interpolation Functions are based on non-uniform torsional differential equations, the analysis of stiffness matrix is facilitated. Therefore, its ability to produce accurate results with the least number of elements i...

Abstract. Experimental observations of univariate rootfinding by generalized companion matrix pencils expressed in the Lagrange basis show that the method can sometimes be numerically stable. It has recently been proved that a new condition number, defined for points on a set containing the interpolation points, is never larger than the rootfinding condition number for the Bernstein polynomial ...

In this paper a new element for analysis of thin-walled structures is presented, and the effects of secondary shear stresses on longitudinal displacements are examined. Since the Interpolation Functions are based on non-uniform torsional differential equations, the analysis of stiffness matrix is facilitated. Therefore, its ability to produce accurate results with the least number of elements i...

The space of upper triangular matrices with Hilbert{Schmidt norm can be viewed as a nite dimensional analogue of the Hardy space H2 of the unit disk when one introduces the adequate notion of \point" evaluation. A bitangential interpolation problem in this setting is studied. The description of all solution in terms of Beurling{Lax representation is given.

This paper is concerned with parametrization issues for rational lossless matrix valued functions. In the same vein as previous works, interpolation theory with metric constraints is used to ensure the lossless property. We consider here boundary interpolation and provide a new parametrization of balanced canonical forms in which the parameters are angular derivatives. We finally investigate th...

A general interpolation problem for operator–valued Stieltjes functions is studied using V. P. Potapov’s method of fundamental matrix inequalities and the method of operator identities. The solvability criterion is established and under certain restrictions the set of all solutions is parametrized in terms of a linear fractional transformation. As applications of a general theory, a number of c...