Piecewise smooth approximations toq-plurisubharmonic functions
نویسندگان
چکیده
منابع مشابه
Optimal Approximations by Piecewise Smooth Functions and Associated Variational Problems
The purpose of this paper is to introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision. In computer vision, a fundamental problem is to appropriately decompose the domain R of a function g ( x , y) of two variables. To explain this problem, we have to start by describing the physical situation whch produces images: ...
متن کاملApproximating Piecewise-Smooth Functions
We consider the possibility of using locally supported quasi-interpolation operators for the approximation of univariate non-smooth functions. In such a case one usually expects the rate of approximation to be lower than that of smooth functions. It is shown in this paper that prior knowledge of the type of ’singularity’ of the function can be used to regain the full approximation power of the ...
متن کاملPiecewise-smooth Refinable Functions
Univariate piecewise-smooth refinable functions (i.e., compactly supported solutions of the equation φ( 2 ) = ∑N k=0 ckφ(x−k)) are classified completely. Characterization of the structure of refinable splines leads to a simple convergence criterion for the subdivision schemes corresponding to such splines, and to explicit computation of the rate of convergence. This makes it possible to prove a...
متن کاملPiecewise-Linear Approximations of Uncertain Functions
We study the problem of approximating a function F : R→ R by a piecewise-linear function F when the values of F at {x1, . . . , xn} are given by a discrete probability distribution. Thus, for each xi we are given a discrete set yi,1, . . . , yi,mi of possible function values with associated probabilities pi,j such that Pr[F(xi) = yi,j ] = pi,j . We define the error of F as error(F,F) = maxi=1 E...
متن کاملBest 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 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: Pacific Journal of Mathematics
سال: 1990
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1990.142.227