Related papers: Local approximation of operators
We consider the popular $k$-means problem in $d$-dimensional Euclidean space. Recently Friggstad, Rezapour, Salavatipour [FOCS'16] and Cohen-Addad, Klein, Mathieu [FOCS'16] showed that the standard local search algorithm yields a…
Finite-sum optimization has wide applications in machine learning, covering important problems such as support vector machines, regression, etc. In this paper, we initiate the study of solving finite-sum optimization problems by quantum…
Fueled by many applications in random processes, imaging science, geophysics, etc., fractional Laplacians have recently received significant attention. The key driving force behind the success of this operator is its ability to capture…
The problem of approximating the covariance operator of the mild solution to a linear stochastic partial differential equation is considered. An integral equation involving the semigroup of the mild solution is derived and a general error…
Structured convex optimization problems typically involve a mix of smooth and nonsmooth functions. The common practice is to activate the smooth functions via their gradient and the nonsmooth ones via their proximity operator. We show that,…
We prove a characterization for the Peetre type $K$-functional on $\mathbb{M}$, a compact two-point homogeneous space, in terms the rate of approximation of a family of multipliers operator defined to this purpose. This extends the well…
We present two approximate versions of the proximal subgradient method for minimizing the sum of two convex functions (not necessarily differentiable). The algorithms involve, at each iteration, inexact evaluations of the proximal operator…
In this paper, we investigate a class of nonconvex and nonsmooth fractional programming problems, where the numerator composed of two parts: a convex, nonsmooth function and a differentiable, nonconvex function, and the denominator consists…
In this paper a local approximation method on the sphere is presented. As interpolation scheme we consider a partition of unity method, such as the modified spherical Shepard's method, which uses zonal basis functions (ZBFs) plus spherical…
This work is concerned with the prime factor decomposition (PFD) of strong product graphs. A new quasi-linear time algorithm for the PFD with respect to the strong product for arbitrary, finite, connected, undirected graphs is derived.…
Consider an $s$-dimensional function being evaluated at $n$ points of a low discrepancy sequence (LDS), where the objective is to approximate the one-dimensional functions that result from integrating out $(s-1)$ variables. Here, the…
In this paper we focus on efficient implementations of the Multivariate Decomposition Method (MDM) for approximating integrals of $\infty$-variate functions. Such $\infty$-variate integrals occur for example as expectations in uncertainty…
The Sum-of-Squares (SOS) approximation method is a technique used in optimization problems to derive lower bounds on the optimal value of an objective function. By representing the objective function as a sum of squares in a feature space,…
In the past decades, the finite difference methods for space fractional operators develop rapidly; to the best of our knowledge, all the existing finite difference schemes, including the first and high order ones, just work on uniform…
Approximation on the spherical cap is different from that on the sphere which requires us to construct new operators. This paper discusses the approximation on the spherical cap. That is, so called Jackson-type operator…
In this paper, we consider optimizing a smooth, convex, lower semicontinuous function in Riemannian space with constraints. To solve the problem, we first convert it to a dual problem and then propose a general primal-dual algorithm to…
Kronecker-factored approximate curvature (KFAC) is arguably one of the most prominent curvature approximations in deep learning. Its applications range from optimization to Bayesian deep learning, training data attribution with influence…
We have developed a method for constructing spectral approximations for convolution operators of Fredholm type. The algorithm we propose is numerically stable and takes advantage of the recurrence relations satisfied by the entries of such…
Several novel imaging and non-destructive testing technologies are based on reconstructing the spatially dependent coefficient in an elliptic partial differential equation from measurements of its solution(s). In practical applications, the…
Fractional order controllers become increasingly popular due to their versatility and superiority in various performance. However, the bottleneck in deploying these tools in practice is related to their analog or numerical implementation.…