Related papers: A sampling-based approximation of the complex erro…
This paper deals with the kernel-based approximation of a multivariate periodic function by interpolation at the points of an integration lattice -- a setting that, as pointed out by Zeng, Leung, Hickernell (MCQMC2004, 2006) and Zeng,…
In order to approximate the integral $I(f)=\int_a^b f(x) dx$, where $f$ is a sufficiently smooth function, models for quadrature rules are developed using a given {\it panel} of $n (n\geq 2)$ equally spaced points. These models arise from…
In this paper, a novel method to adaptively approximate the solution to stochastic differential equations, which is based on compressive sampling and sparse recovery, is introduced. The proposed method consider the problem of sparse…
The Sinc approximation has shown high efficiency for numerical methods in many fields. Conformal maps play an important role in the success, i.e., appropriate conformal map must be employed to elicit high performance of the Sinc…
Unitary best approximation to the exponential function on an interval on the imaginary axis has been introduced recently. In the present work two algorithms are considered to compute this best approximant: an algorithm based on rational…
This paper explores the possibilities and limitations of error correction by the structural simplicity of error mechanisms. Specifically, we consider channel models, called \emph{samplable additive channels}, in which (a) errors are…
The approximation of a high-dimensional vector by a small combination of column vectors selected from a fixed matrix has been actively debated in several different disciplines. In this paper, a sampling approach based on the Monte Carlo…
The paper presents the derivation of the asymptotic behavior of $\nu$-zeros of the modified Bessel function of imaginary order $K_{{\rm i}\nu}(z)$. This derivation is based on the quasiclassical treatment of the exponential potential on the…
While the theory of operator approximation with any given accuracy is well elaborated, the theory of {best constrained} constructive operator approximation is still not so well developed. Despite increasing demands from applications this…
A numerical algorithm (implemented in Matlab) for computing the zeros of the parabolic cylinder function $U(a,z)$ in domains of the complex plane is presented. The algorithm uses accurate approximations to the first zero plus a highly…
Probabilistic inference is fundamentally hard, yet many tasks require optimization on top of inference, which is even harder. We present a new optimization-via-compilation strategy to scalably solve a certain class of such problems. In…
In this paper, several modifications are introduced to the functional approximation method iterLap to reduce the approximation error, including stopping rule adjustment, proposal of new residual function, starting point selection for…
We propose an extrapolation technique that allows accuracy improvement of the discrete dipole approximation computations. The performance of this technique was studied empirically based on extensive simulations for 5 test cases using many…
We investigate quantum computational complexity of calculating partition functions of Ising models. We construct a quantum algorithm for an additive approximation of Ising partition functions on square lattices. To this end, we utilize the…
For the nonparametric regression models with covariates contaminated with normal measurement errors, this paper proposes an extrapolation algorithm to estimate the nonparametric regression functions. By applying the conditional expectation…
Several applications of slicing require a program to be sliced with respect to more than one slicing criterion. Program specialization, parallelization and cohesion measurement are examples of such applications. These applications can…
We present a new algorithm to compute minimal telescopers for rational functions in two discrete variables. As with recent reduction-based approaches, our algorithm has the important feature that the computation of a telescoper is…
The paper proposes an approximate expression for calculating very complex one-dimensional integrals depending on the parameter $a$. These integrals often occur in computational problems theory of magnetic solitons. The resulting analytical…
We describe and analyze a simple algorithm for sampling from the solution $\mathbf{x}^* := \mathbf{A}^+\mathbf{b}$ to a linear system $\mathbf{A}\mathbf{x} = \mathbf{b}$. We assume access to a sampler which allows us to draw indices…
A sampling-based optimization method for quadratic functions is proposed. Our method approximately solves the following $n$-dimensional quadratic minimization problem in constant time, which is independent of $n$: $z^*=\min_{\mathbf{v} \in…