Related papers: Parquet Approximation in Large $N$ Matrix Theories
Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization can be solved very efficiently by standard algorithms in practice. However, due to the non-convexity…
We give a new proof for an equality of certain max-min and min-max approximation problems involving normal matrices. The previously published proofs of this equality apply tools from matrix theory, (analytic) optimization theory and…
Parameterization and approximation are two popular ways of coping with NP-hard problems. More recently, the two have also been combined to derive many interesting results. We survey developments in the area both from the algorithmic and…
A novel matrix approximation problem is considered herein: observations based on a few fully sampled columns and quasi-polynomial structural side information are exploited. The framework is motivated by quantum chemistry problems wherein…
In paper a new definition of reduced Pade approximant and algorithm for its computing is proposed. Our approach is based on the investigation of the kernel structure of the Toeplitz matrix. It is shown that the reduced Pade approximant…
The inverse of a large matrix can often be accurately approximated by a polynomial of degree significantly lower than the order of the matrix. The iteration polynomial generated by a run of the GMRES algorithm is a good candidate, and its…
Finite difference schemes are here solved by means of a linear matrix equation. The theoretical study of the related algebraic system is exposed, and enables us to minimize the error due to a finite difference approximation, while building…
Approximate linear programming (ALP) is an efficient approach to solving large factored Markov decision processes (MDPs). The main idea of the method is to approximate the optimal value function by a set of basis functions and optimize…
We introduce the concept of matrix liberation process, a random matrix counterpart of the liberation process in free probability, and prove a large deviation upper bound for its empirical distribution with several properties on its rate…
We introduce the notion of an approximation system as a generalization of Taylor approximation, and we give some first examples. Next we develop the general theory, including error bounds and a sufficient criterion for convergence. More…
We address the problem of minimizing a convex function over the space of large matrices with low rank. While this optimization problem is hard in general, we propose an efficient greedy algorithm and derive its formal approximation…
Given a graph, the general problem to cover the maximum number of vertices by a collection of vertex-disjoint long paths seemingly escapes from the literature. A path containing at least $k$ vertices is considered long. When $k \le 3$, the…
A generalization of recent group-theoretic matrix multiplication algorithms to an analogue of the theory of partial matrix multiplication is presented. We demonstrate that the added flexibility of this approach can in some cases improve…
In this experimental study we consider Steiner tree approximations that guarantee a constant approximation of ratio smaller than $2$. The considered greedy algorithms and approaches based on linear programming involve the incorporation of…
We give unique recovery guarantees for matrices of bounded rank that have undergone permutations of their entries. We even do this for a more general matrix structure that we call ladder matrices. We use methods and results of commutative…
Matrix functions are a central topic of linear algebra, and problems requiring their numerical approximation appear increasingly often in scientific computing. We review various limited-memory methods for the approximation of the action of…
Consider the following optimization problem: Given $n \times n$ matrices $A$ and $\Lambda$, maximize $\langle A, U\Lambda U^*\rangle$ where $U$ varies over the unitary group $\mathrm{U}(n)$. This problem seeks to approximate $A$ by a matrix…
Rough set theory is a useful tool to deal with uncertain, granular and incomplete knowledge in information systems. And it is based on equivalence relations or partitions. Matroid theory is a structure that generalizes linear independence…
In this talk results of study in various dimensions of the Boltzmann master field for a subclass of planar diagrams, so called half-planar diagrams, found in the recent work by Accardi, Volovich and one of us (I.A.) are presented.
Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…