Related papers: Mathematical Construction of Interpolation and Ext…
The use of regression analysis for processing experimental data is fraught with certain difficulties, which, when models are constructed, are associated with assumptions, and there is a normal law of error distribution and variables are…
One way to investigate the precision of estimates likely to result from planned experiments and planned epidemiological studies is to simulate a large number of possible outcomes and analyse the sets of possible results. This appears to be…
In this paper we consider the approximation of a function by its interpolating multilinear spline and the approximation of its derivatives by the derivatives of the corresponding spline. We derive formulas for the uniform approximation…
A retrieval model should not only interpolate the training data but also extrapolate well to the queries that are different from the training data. While neural retrieval models have demonstrated impressive performance on ad-hoc search…
The interpolation-regression approximation is a powerful tool in numerical analysis for reconstructing functions defined on square or triangular domains from their evaluations at a regular set of nodes. The importance of this technique lies…
In mesh-based numerical simulations, the interpolation of mesh-defined functions across different meshes is a critical task, and achieving high-precision interpolation is of great significance for improving the computational efficiency and…
We use elliptic Taylor series expansions and interpolation to deduce a number of summations for elliptic hypergeometric series. We extend to the well-poised elliptic case results that in the $q$-case have previously been obtained by Cooper…
In this survey article some classical results concerning real interpolation between Hardy spaces are briefly presented and then it is explained how those results can be used to establish Yano-type extrapolation theorems for Hardy spaces.…
In this paper we study interpolation in local extensions of a base theory. We identify situations in which it is possible to obtain interpolants in a hierarchical manner, by using a prover and a procedure for generating interpolants in the…
Let $T$ be an arbitrary operator bounded from $L^{p_0}(w)$ into $L^{p_0, \infty}(w)$ for every weight $w$ in the Muckenhoupt class $A_{p_0}$. It is proved in this article that the distribution function of $Tf$ with respect to any weight $u$…
Model merging, typically on Instruct and Thinking models, has shown remarkable performance for efficient reasoning. In this paper, we systematically revisit the simplest merging method that interpolates two weights directly. Particularly,…
The purpose of this paper is to construct p-adic analytically continued function which interpolates q-Euler numbers at negative integer Finally, we give an explicit p-adic expansion as a power series in n.
The paper suggests a method of extrapolation of notion of one-sided semi-infinite sequences representing traces of two-sided band-limited sequences; this features ensure uniqueness of this extrapolation and possibility to use this for…
Using the reflection formula of the Gamma function, we derive a new formula for the Taylor coefficients of the reciprocal Gamma function. The new formula provides effective asymptotic values for the coefficients even for very small values…
This work investigates theoretically the interplay between interpolation and aggregation in regression. We establish that the $\gamma$-graph dimension characterizes learnability for a broad class of natural aggregation procedures.…
In this work we consider a model problem of deep neural learning, namely the learning of a given function when it is assumed that we have access to its point values on a finite set of points. The deep neural network interpolant is the the…
In this document I develop a weight function theory of positive order basis function interpolants and smoothers. **In Chapter 1 the basis functions and data spaces are defined directly using weight functions. The data spaces are used to…
Taylor's formula holds significant importance in function representation, such as solving differential difference equations, ordinary differential equations, partial differential equations, and further promotes applications in visual…
In this paper we introduce a family of rational approximations of the reciprocal of a $\phi$-function involved in the explicit solutions of certain linear differential equations, as well as in integration schemes evolving on manifolds. The…
This paper describes the practical application of causal extrapolation of sequences for the purpose of forecasting. The methods and proofs have been applied to simulations to measure the range which data can be accurately extrapolated. Real…