Abstract. Some prediction properties of the t-transformation of Levin are analyzed for two kinds of limiting processes. It is shown under certain circumstances that when the t-transformation is applied to a power series, the coefficients of the Maclaurin series of the rational approximation obtained approximate those of the given series with increasing accuracy. Theoretical and numerical exampl...

A connection is established between uniform rational approximation and approximation in the mean by polynomials on compact nowhere dense subsets of the complex plane C. Peak points for R(X) and bounded point evaluations for Hp(X, dA), 1 ≤ p < ∞, play a fundamental role.

1 On the so–called Pell–Fermat equation 2 1.1 Examples of simple continued fractions . . . . . . . . . . . . . 2 1.2 Existence of integer solutions . . . . . . . . . . . . . . . . . . 5 1.3 All integer solutions . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 On the group of units of Z[ √ D] . . . . . . . . . . . . . . . . . 8 1.5 Connection with rational approximation . . . . . . . . . . ....

A new method for construction of bases for general distribution spaces is developed. This method allows the freedom to prescribe the nature and properties of the basis elements. The method is deployed to the construction of bases consisting of rational functions of uniformly bounded degrees for Besov and Triebel–Lizorkin spaces of holomorphic functions in the unit disc. In turn, this is utilize...

We study nonlinear approximation in Lp(R) (0 < p < ∞, d > 1) from (a) n-term rational functions, and (b) piecewise polynomials generated by different anisotropic dyadic partitions of Rd. To characterize the rates of each such piecewise polynomial approximation we introduce a family of smoothness spaces (B-spaces) which can be viewed as an anisotropic variation of Besov spaces. We use the B-spac...

A strong error estimate for the uniform rational approximation of xa on [0, 1] is given, and its proof is sketched. Let E„n(xa, [0, 1]) denote the minimal approximation error in the uniform norm. Then it is shown that lim e2*^"Enn(xa , [0, 1]) = 41+a| sin7ta| n—»oo holds true for each a > 0 .

In this work we bring together classical mechanism theory with recent works in the area of Computer Aided Geometric Design(CAGD) of rational motions as well as curve approximation techniques in CAGD to study the problem of mechanism motion approximation from a computational geometric viewpoint. We present a framework for approximating algebraic motions of spherical mechanisms with rational B-Sp...