Related papers: Upper bounds for the error in some interpolation a…
An upper bound for the Lebesgue constant (the supremum norm) of the operator of interpolation of a function in equally spaced points of a triangle by a polynomial of total degree less than or equal to n is obtained. Earlier, the rate of…
The primary objective of this study is to develop novel interpolation operators that interpolate the boundary values of a function defined on a triangle. This is accomplished by constructing New Generalized Boolean sum neural network…
We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in…
We consider the problem of obtaining interpolation constraints for function classes, i.e., necessary and sufficient constraints that a set of points, function values and (sub)gradients must satisfy to ensure the existence of a global…
If uncertainty is modelled by a probability measure, decisions are typically made by choosing the option with the highest expected utility. If an imprecise probability model is used instead, this decision rule can be generalised in several…
Let $B_n$ be the Euclidean unit ball in ${\mathbb R}^n$ given by the inequality $\|x\|\leq 1$, $\|x\|:=\left(\sum\limits_{i=1}^n x_i^2\right)^{\frac{1}{2}}$. By $C(B_n)$ we mean the space of continuous functions $f:B_n\to{\mathbb R}$ with…
We consider the problem of modulation and estimation of a random parameter $U$ to be conveyed across a discrete memoryless channel. Upper and lower bounds are derived for the best achievable exponential decay rate of a general moment of the…
In the era of big data, we first need to manage the data, which requires us to find missing data or predict the trend, so we need operations including interpolation and data fitting. Interpolation is a process to discover deducing new data…
In this paper, we improve the usual relative error bound for the computation of x^n through iterated multiplications by x in binary floating-point arithmetic. The obtained error bound is only slightly better than the usual one, but it is…
An extension of sinc interpolation on $\mathbb{R}$ to the class of algebraically decaying functions is developed in the paper. Similarly to the classical sinc interpolation we establish two types of error estimates. First covers a wider…
For the general parametric regression models with covariates contaminated with normal measurement errors, this paper proposes an accelerated version of the classical simulation extrapolation algorithm to estimate the unknown parameters in…
Error estimation of difference operators on irregular nodes is discussed. We can obtain the similar estimates of the errors. However, the error estimate for the difference operators for the second derivatives becomes lower because of…
Based on a new Taylor-like formula, we derived an improved interpolation error estimate in $W^{1,p}$. We compare it with the classical error estimates based on the standard Taylor formula, and also with the corresponding interpolation error…
The challenge to measure exposures regularly forces financial institutions into a choice between an overwhelming computational burden or oversimplification of risk. To resolve this unsettling dilemma, we systematically investigate replacing…
In the 1990's exponential-type error bounds appeared in the theory of radial basis functions. This kind of error bounds is very powerful. However it only measures the difference between the approximant and approximand. Mathematicians and…
We consider the problem of determining, within an elastic isotropic nanoplate in bending, the possible presence of an inclusion made of different elastic material. Under suitable a priori assumptions on the unknown inclusion, we provide…
This paper provides data-dependent bounds on the expected error of the Gibbs algorithm in the overparameterized interpolation regime, where low training errors are also obtained for impossible data, such as random labels in classification.…
Stochastic optimization often involves calculating the expected value of a first-order max or min function, known as a first-order loss function. In this context, loss functions are frequently approximated using piecewise linear functions.…
It's well-known that there is a very powerful error bound for Gaussians put forward by Madych and Nelson in 1992. It's of the form$% | f(x)-s(x)| \leq (Cd)^{\frac{c}{d}}\left\Vert f\right\Vert_{h}$ where $C,c$ are constants, $h$ is the…
Interpolating functional method is a powerful tool for studying the behavior of a quantity in the intermediate region of the parameter space of interest by using its perturbative expansions at both ends. Recently several interpolating…