We start by clarifying the terms which appear in the title. For a given theory of selfinteracting quantum fields, by Gaussian approximation we mean the Gaussian part of the interacting measure. By mean field approximation we understand the leading term of the expansion given in [1, 2] and by variational approximation we understand the old variational technique performed with some particular tri...

We consider maximizing a monotone submodular function under cardinality constraint or knapsack in the streaming setting. In particular, elements arrive sequentially and at any point of time, algorithm has access to only small fraction data stored primary memory. propose following algorithms taking O(ε− 1) passes: (1) (1 − e− 1 ε)-approximation for cardinality-constrained problem, (2) (0.5 knaps...

The saddlepoint approximation gives an to the density of a random variable in terms its moment generating function. When underlying is itself sum n unobserved i.i.d. terms, basic classical result that relative error order 1/n. If instead interpreted as likelihood and maximised function model parameters, maximum estimate (MLE) can be much faster compute than true MLE. This paper proves analogous...

Nonstandard finite difference schemes for the Black-Scholes partial differential equation preserving the positivity property are proposed. Computationally simple schemes are derived by using a nonlocal approximation in the reaction term of the Black-Scholes equation. Unlike the standard methods, the solutions of new proposed schemes are positive and free of the spurious oscillations.

In a continuation of recent work on Besov regularity of solutions to elliptic PDEs in Lipschitz domains with polyhedral structure, we prove an embedding between weighted Sobolev spaces (Kondratiev spaces) relevant for the regularity theory for such elliptic problems, and TriebelLizorkin spaces, which are known to be closely related to approximation spaces for nonlinear n-term wavelet approximat...

In the present paper, we study nonlinear approximation properties of multivariate wavelet biframes. For a certain range of parameters, the approximation classes associated with best N term approximation are determined to be Besov spaces and thresholding the wavelet bi-frame expansion realizes the approximation rate. Our findings extend results about dyadic wavelets to more general scalings. Fin...

In this paper, we develop a robust fast method for mobile-immobile variable-order (VO) time-fractional diffusion equations (tFDEs), superiorly handling the cases of small or vanishing lower bound VO function. The valid approximation Caputo fractional derivative is obtained using integration by parts and exponential-sum-approximation method. Compared with general direct method, proposed algorith...

Restricted non-linear approximation is a type of N-term approximation where a measure ν on the index set (rather than the counting measure) is used to control the number of terms in the approximation. We show that embeddings for restricted non-linear approximation spaces in terms of weighted Lorentz sequence spaces are equivalent to Jackson and Bernstein type inequalities, and also to the upper...

introduction :   co 2 (carbon dioxide) laser application in circumcision, for cutting and coagulation, has been reported to have excellent results. also, tissue glue has been reported to have advantages over sutures for approximation of wound edges. most previous studies focused on comparisons between co 2 laser and scalpel, or between tissue glue and sutures. this study prospectively compared ...