We obtain various estimates for the error in adaptive approximation and also establish a relationship between adaptive approximation and free-knot spline approximation.

We prove that if f is increasing on [ 1,1], then for each n = 1, 2 . . . . . there is an increasing algebraic polynomial P. of degree n such that {f(x) P.(x){ < cw2( f, V/I x 2 /n) , where w2 is theâ€¦ (More)

We prove that if a function f 2 C0; 1] changes sign nitely many times, then for any n large enough the degree of copositive approximation to f by quadratic splines with n?1 equally spaced knots canâ€¦ (More)

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,â€¦ (More)

We estimate the error in approximating a function f by rational functions of degree n in the norm of Lq(Q), Q := [0,1]d. Among other things, we prove that if f is in the Sobolev space Wk(Q) and ifâ€¦ (More)

Our study of perfect spline approximation reveals: (i) it is closely related to Î£âˆ† modulation used in one-bit quantization of bandlimited signals. In fact, they share the same recursive formulae,â€¦ (More)

We obtain the characterization of saturation class and approximation spaces for perfect spline approximation. Also, a generalized perfect spline approximation is investigated.

It is well known that the adaptive algorithm is simple and easy to program but the results are not fully competitive with other nonlinear methods such as free knot spline approximation. We modify theâ€¦ (More)