Add to ORKGA necessary condition for a best Chebyshev approximation by piecewise linear functions is derived using quasidifferential calculus. We first discover some properties of the knots joining the linear functions. Then we use these properties to obtain the optimality condition. This condition is stronger than existing results. We present an example of linear spline approximation where the existing optimality conditions are satisfied, but not the proposed one, which shows that it is not optimal. Copyright © 2010 Watam Press
In this paper necessary and sufficient optimality conditions for uniform approximation of continuous...
It has been shown (by Lutterkort, Peters and Reif) that the problem of best approximation of a polyn...
In this paper, we derive a necessary condition for a best approximation by piecewise polynomial func...
A necessary condition for a best Chebyshev approximation by piecewise linear functions is derived us...
In this paper, we study the problem of best Chebyshev approximation by linear splines. We construct ...
In this paper, we derive conditions for best uniform approximation by fixed knots polynomial splines...
In this paper, we derive a necessary condition for a best approximation by piecewise polynomial func...
AbstractThis paper is concerned with Chebyshev approximation by spline functions with free knots. If...
In this paper, we derive a necessary condition for a best approximation by piecewise polynomial func...
AbstractThe problem of approximating a given function by spline functions with fixed knots is discus...
AbstractAn algorithm is developed which computes strict approximations in subspaces of spline functi...
We consider the problem of finding the best (uniform) approximation of a given continuous function b...
One of the purposes in this paper is to provide a better understanding of the alternance property wh...
AbstractWe prove that the best one-sided L1 approximation by splines with fixed knots to a different...
In 1957, E. Ya. Remez published a monograph devoted to numerical methods of Chebyshev approximation...
In this paper necessary and sufficient optimality conditions for uniform approximation of continuous...
It has been shown (by Lutterkort, Peters and Reif) that the problem of best approximation of a polyn...
In this paper, we derive a necessary condition for a best approximation by piecewise polynomial func...
A necessary condition for a best Chebyshev approximation by piecewise linear functions is derived us...
In this paper, we study the problem of best Chebyshev approximation by linear splines. We construct ...
In this paper, we derive conditions for best uniform approximation by fixed knots polynomial splines...
In this paper, we derive a necessary condition for a best approximation by piecewise polynomial func...
AbstractThis paper is concerned with Chebyshev approximation by spline functions with free knots. If...
In this paper, we derive a necessary condition for a best approximation by piecewise polynomial func...
AbstractThe problem of approximating a given function by spline functions with fixed knots is discus...
AbstractAn algorithm is developed which computes strict approximations in subspaces of spline functi...
We consider the problem of finding the best (uniform) approximation of a given continuous function b...
One of the purposes in this paper is to provide a better understanding of the alternance property wh...
AbstractWe prove that the best one-sided L1 approximation by splines with fixed knots to a different...
In 1957, E. Ya. Remez published a monograph devoted to numerical methods of Chebyshev approximation...
In this paper necessary and sufficient optimality conditions for uniform approximation of continuous...
It has been shown (by Lutterkort, Peters and Reif) that the problem of best approximation of a polyn...
In this paper, we derive a necessary condition for a best approximation by piecewise polynomial func...