相关论文: Vandermonde with Arnoldi

We construct a convergent family of outer approximations for the problem of optimizing polynomial functions over convex bodies subject to polynomial constraints. This is achieved by generalizing the polarization hierarchy, which has…

In order to perform faster simulations, the model reduction is nowadays used in industrial contexts to solve large and complex problems. However, the efficiency of such an approach is sometimes cut by the interface size of the reduced model…

Low-rank optimization problems with sparse simplex constraints involve variables that must satisfy nonnegativity, sparsity, and sum-to-1 conditions, making their optimization particularly challenging due to the interplay between low-rank…

Quadratic programming over orthogonal matrices encompasses a broad class of hard optimization problems that do not have an efficient quantum representation. Such problems are instances of the little noncommutative Grothendieck problem…

In this article, we introduce and study accelerated Landweber methods for linear ill-posed problems obtained by an alteration of the coefficients in the three-term recurrence relation of the \nu-methods. The residual polynomials of the…

We show that the condition number of any cyclically contiguous $p\times q$ submatrix of the $N\times N$ discrete Fourier transform (DFT) matrix is at least $$ \exp \left( \frac{\pi}{2} \left[\min(p,q)- \frac{pq}{N}\right] \right)~, $$ up to…

We extend the Frank-Wolfe (FW) optimization algorithm to solve constrained smooth convex-concave saddle point (SP) problems. Remarkably, the method only requires access to linear minimization oracles. Leveraging recent advances in FW…

We study the existing algorithms that solve the multidimensional martingale optimal transport. Then we provide a new algorithm based on entropic regularization and Newton's method. Then we provide theoretical convergence rate results and we…

A novel orthogonalization-free method together with two specific algorithms are proposed to solve extreme eigenvalue problems. On top of gradient-based algorithms, the proposed algorithms modify the multi-column gradient such that earlier…

We consider an iterative eigensolver for Schr\"odinger equations that constructs low-rank approximations of eigenfunctions with accuracy-adapted ranks, with particular focus on fermionic Schr\"odinger equations in second-quantized form and…

The robust adjustment of nonlinear models to data is considered in this paper. When data comes from real experiments, it is possible that measurement errors cause the appearance of discrepant values, which should be ignored when adjusting…

In this research, the Bernoulli polynomials are introduced. The properties of these polynomials are employed to construct the operational matrices of integration together with the derivative and product. These properties are then utilized…

Meaningful comparison between sets of observations often necessitates alignment or registration between them, and the resulting optimization problems range in complexity from those admitting simple closed-form solutions to those requiring…

We comment on two randomized algorithms for constructing low-rank matrix decompositions. Both algorithms employ the Subsampled Randomized Hadamard Transform [14]. The first algorithm appeared recently in [9]; here, we provide a novel…

In this paper, we achieve three primary objectives related to the rigorous computational analysis of nonlinear PDEs posed on complex geometries such as disks and cylinders. First, we introduce a validated Matrix Multiplication Transform…

Recent literature has advocated the use of randomized methods for accelerating the solution of various matrix problems arising throughout data science and computational science. One popular strategy for leveraging randomization is to use it…

Motivated by a certain molecular reconstruction methodology in cryo-electron microscopy, we consider the problem of solving a linear system with two unknown orthogonal matrices, which is a generalization of the well-known orthogonal…

In this paper we use the Vandermonde matrices and their properties to give a new proof of the classical result of Karl Weierstrass about the approximation of continuous functions $f$ on closed intervals, using a sequence of polynomials. The…

Theoretical estimates of the convergence rate of many well-known gradient-type optimization methods are based on quadratic interpolation, provided that the Lipschitz condition for the gradient is satisfied. In this article we obtain a…

Motivated by numerical methods for solving parametric partial differential equations, this paper studies the approximation of multivariate analytic functions by algebraic polynomials. We introduce various anisotropic model classes based on…