Practical $L\sp p$ polynomial approximation

Polynomial Approximation in Lt , ( 0 < p < 1 )

We are interested in the approximation of functions f ~ Lp(I), 0 < p < 1, I = [ 1 , 1], by algebraic polynomials. Such approximation has previously been studied by other authors, most notably, Storozhenko, Krotov, and Oswald [-S-K-O] and Khodak [K]. Our main departure from these previous works is that we shall prove direct estimates for the error of polynomial approximation in terms of the Ditz...

On Padé Approximation of Some Practical Functions

NP=P: From Polynomial Time Approximation Bounded Solutions of TSP

The question of whether all problems in NP class are also in P class is generally considered one of the most important open questions in mathematics and theoretical computer science as it has far-reaching consequences to other problems in mathematics, computer science, biology, philosophy and cryptography. There are intensive research on proving ‘NP not equal to P’ and ‘NP equals to P’. However...

Convex Polynomial and Spline Approximation in Lp , 0 < p <

We prove that a convex function f 6 L p [ -1 , 1], 0 < p < cx~, can be approximated by convex polynomials with an error not exceeding Cw~ (f, 1/n)p where w~(f, .) is the Ditzian-Totik modulus of smoothness of order three of f . We are thus filling the gap between previously known estimates involving og~(f, I/n)p, and the impossibility of having such estimates involving ~o4. We also give similar...

Polynomial Approximation

Polynomials are very simple mathematical functions which have the flexibility to represent very general nonlinear relationships. Approximation of more complicated functions by polynomials is a basic building block for many numerical techniques. This article considers two distinct but related applications. The first is polynomial regression in which polynomials are used to model a nonlinear rela...