Optimal algorithms for doubly weighted approximation of univariate functions

Frequency-weighted optimal Hankel-norm approximation of stable transfer functions

The present paper presents a method of frequency shaping the error obtained by performing an optimal Hankel-norm approximation of a scalar, finite-dimensional, linear, time-invariant system. The optimal Hankel-norm approximation procedure finds a transfer function (or transfer function matrix) of prescribed order which approximates a given transfer function (or transfer function matrix) of grea...

On error formulas for approximation by sums of univariate functions

The purpose of the paper is to develop a new method for obtaining explicit formulas for the error of approximation of bivariate functions by sums of univariate functions. It should be remarked that formulas of this type have been known only for functions defined on a rectangle with sides parallel to coordinate axes. Our method, based on a maximization process over closed bolts, allows the consi...

Optimal Approximation of Functions

Efficient Approximation Algorithms for Weighted b-Matching

We describe a half-approximation algorithm, b-Suitor, for computing a b-Matching of maximum weight in a graph with weights on the edges. b-Matching is a generalization of the well-known Matching problem in graphs, where the objective is to choose a subset of M edges in the graph such that at most a specified number b(v) of edges in M are incident on each vertex v. Subject to this restriction we...

Approximation of Univariate Set-Valued Functions- an Overview

The paper is an updated survey of our work on the approximation of univariate setvalued functions by samples-based linear approximation operators, beyond the results reported in our previous overview. Our approach is to adapt operators for real-valued functions to set-valued functions, by replacing operations between numbers by operations between sets. For set-valued functions with compact conv...