相关论文: Minimizing Squared Vertical and Squared Horizontal…

For a probability measure on a real separable Hilbert space, we are interested in "volume-based" approximations of the d-dimensional least squares error of it, i.e., least squares error with respect to a best fit d-dimensional affine…

In this paper we present an algorithm to reduce the area of a surface spanned by a finite number of boundary curves by initiating a variational improvement in the surface. The ansatz we suggest consists of original surface plus a…

In this paper, we minimize the self-centered smoothed gap, a recently introduced optimality measure, in order to solve convex-concave saddle point problems. The self-centered smoothed gap can be computed as the sum of a convex, possibly…

We present computational methods for constructing orthogonal/orthonormal polynomials over arbitrary polygonal domains in $\mathbb{R}^2$ using bivariate spline functions. Leveraging a mature MATLAB implementation which generates spline…

A solution manifold is the collection of points in a $d$-dimensional space satisfying a system of $s$ equations with $s<d$. Solution manifolds occur in several statistical problems including hypothesis testing, curved-exponential families,…

We study the optimality of the minimax risk of truncated series estimators for symmetric convex polytopes. We show that the optimal truncated series estimator is within $O(\log m)$ factor of the optimal if the polytope is defined by $m$…

Motivated by applications in robotics and computer vision, we study problems related to spatial reasoning of a 3D environment using sublevel sets of polynomials. These include: tightly containing a cloud of points (e.g., representing an…

In this paper, we issue an error analysis for integration over discrete surfaces using the surface parametrization presented in [PS22] as well as prove why even-degree polynomials exhibit a higher convergence rate than odd-degree…

We study a popular algorithm for fitting polynomial curves to scattered data based on the least squares with gradient weights. We show that sometimes this algorithm admits a substantial reduction of complexity, and, furthermore, find…

The well-known result states that the square-free counting function up to $N$ is $N/\zeta(2)+O(N^{1/2})$. This corresponds to the identity polynomial $\text{Id}(x)$. It is expected that the error term in question is…

There is proposed a method for improving the convergence of Fourier series by function systems, orthogonal at the segment, the application of which allows for smooth functions to receive uniformly convergent series. There is also proposed…

The paper deals with two fundamental types of trigonometric polynomials and splines on uniform grids, which allow us to construct interpolation approximations that depend linearly on the values of the interpolated function. Fundamental on…

We extend the existing skew polynomial representations of matrix algebras which are direct sum of matrix spaces over division rings. In this representation, the sum-rank distance between two tuples of matrices is captured by a weight…

In this work we propose a simple but effective high order polynomial correction allowing to enhance the consistency of all kind of boundary conditions for the Euler equations (Dirichlet, characteristic far-field and slip-wall), both in 2D…

We describe polynomials of the best uniform approximation to sgn(x) on the union of two intervals in terms of special conformal mappings. This permits us to find the exact asymptotic behavior of the error of this approximation.

A systematic construction of higher order splines using two hierarchies of polynomials is presented. Explicit instructions on how to implement one of these hierarchies are given. The results are limited to interpolations on regular,…

The least square solution of minimum norm of a rectangular linear system of equations can be found out iteratively by using matrix splittings. However, the convergence of such an iteration scheme arising out of a matrix splitting is…

We consider the problem of minimizing a sum of several convex non-smooth functions. We introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple…

Approximation theory plays a central role in numerical analysis, undergoing continuous evolution through a spectrum of methodologies. Notably, Lebesgue, Weierstrass, Fourier, and Chebyshev approximations stand out among these methods.…

We study two important operations on polynomials defined over complete discrete valuation fields: Euclidean division and factorization. In particular, we design a simple and efficient algorithm for computing slope factorizations, based on…