Best rational product approximations of functions
نویسندگان
چکیده
منابع مشابه
Best Approximations by Smooth Functions
THEOREM 1.1 (U. Sattes). Let r > 2 and g E C[O, l]\B$,‘. Then f”EB$’ is a best approximation to g, in L” (such a best approximation necessari/J) exisrs) if and only if there exists a subinterual (a, /?) c IO. 1 I and a positilse integer M > r + 1 for which the following conditions hold (i) f”l,n.ll, is a Perfect spline of degree r with exactly) M ~ r -1 knots arzd I.f”““(s)l = I a. e. on [u,pI....
متن کاملBest Quadratic Approximations of Cubic Boolean Functions
The problem of computing best low order approximations of Boolean functions is treated in this paper. We focus on the case of best quadratic approximations of a wide class of cubic functions of arbitrary number of variables, and provide formulas for their efficient calculation. Our methodology is developed upon Shannon’s expansion formula and properties of best affine approximations of quadrati...
متن کاملFunctions with prescribed best linear approximations
A common problem in applied mathematics is that of finding a function in a Hilbert space with prescribed best approximations from a finite number of closed vector subspaces. In the present paper we study the question of the existence of solutions to such problems. A finite family of subspaces is said to satisfy the Inverse Best Approximation Property (IBAP) if there exists a point that admits a...
متن کاملThe best uniform polynomial approximation of two classes of rational functions
In this paper we obtain the explicit form of the best uniform polynomial approximations out of Pn of two classes of rational functions using properties of Chebyshev polynomials. In this way we present some new theorems and lemmas. Some examples will be given to support the results.
متن کاملRates of Best Uniform Rational Approximation of Analytic Functions by Ray Sequences of Rational Functions
In this paper, problems related to the approximation of a holomorphic function f on a compact subset E of the complex plane C by rational functions from the class Rn,m of all rational functions of order (n,m) are considered. Let ρn,m = ρn,m( f ; E) be the distance of f in the uniform metric on E from the class Rn,m . We obtain results characterizing the rate of convergence to zero of the sequen...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1973
ISSN: 0021-9045
DOI: 10.1016/0021-9045(73)90095-6