相关论文: An adaptive cubic regularization method for comput…

We design a fast implicit real QZ algorithm for eigenvalue computation of structured companion pencils arising from linearizations of polynomial rootfinding problems. The modified QZ algorithm computes the generalized eigenvalues of an…

Cubic invariants for two-dimensional Hamiltonian systems are investigated using the Jacobi geometrization procedure. This approach allows for a unified treatment of invariants at both fixed and arbitrary energy. In the geometric picture the…

This paper studies nuclear norms of symmetric tensors. As recently shown by Friedland and Lim, the nuclear norm of a symmetric tensor can be achieved at a symmetric decomposition. We discuss how to compute symmetric tensor nuclear norms,…

This paper is a survey on exponential integrators to solve cubic-quintic complex Ginzburg-Landau equations and related stiff problems. In particular, we are interested in accurate computation near the pulsating and exploding soliton…

Random tensor models have applications in a variety of fields, such as quantum gravity, quantum information theory, mathematics of modern technologies, etc., and studying their statistical properties, e.g., tensor eigenvalue/vector…

Nontrivial fixed points of the hierarchical renormalization group are computed by numerically solving a system of quadratic equations for the coupling constants. This approach avoids a fine tuning of relevant parameters. We study the…

We consider a statistical model for finite-rank symmetric tensor factorization and prove a single-letter variational expression for its asymptotic mutual information when the tensor is of even order. The proof applies the adaptive…

We consider adaptive finite element methods for second-order elliptic PDEs, where the arising discrete systems are not solved exactly. For contractive iterative solvers, we formulate an adaptive algorithm which monitors and steers the…

For solving large-scale non-convex problems, we propose inexact variants of trust region and adaptive cubic regularization methods, which, to increase efficiency, incorporate various approximations. In particular, in addition to approximate…

The computation of eigenvalues of large-scale matrices arising from finite element discretizations has gained significant interest in the last decade. Here we present a new algorithm based on slicing the spectrum that takes advantage of the…

This paper addresses the optimization problem of minimizing non-convex continuous functions, which is relevant in the context of high-dimensional machine learning applications characterized by over-parametrization. We analyze a randomized…

An algorithm of the tensor renormalization group is proposed based on a randomized algorithm for singular value decomposition. Our algorithm is applicable to a broad range of two-dimensional classical models. In the case of a square…

We present an iterative method for the search of extreme entries in low-rank tensors which is based on a power iteration combined with a binary search. In this work we use the HT-format for low-rank tensors but other low-rank formats can be…

Finding a Z-eigenpair of a symmetric tensor is equivalent to finding a KKT point of a sphere constrained minimization problem. Based on this equivalency, in this paper, we first propose a class of iterative methods to get a Z-eigenpair of a…

In this paper we propose efficient randomized fixed-precision techniques for low tubal rank approximation of tensors. The proposed methods are faster and more efficient than the existing fixed-precision algorithms for approximating the…

An $n \times n \times p$ tensor is called a T-square tensor. It arises from many applications, such as the image feature extraction problem and the multi-view clustering problem. We may symmetrize a T-square tensor to a T-symmetric tensor.…

In this paper, three high-accuracy methods for eigenvalues of second order elliptic operators are proposed by using the nonconforming Crouzeix-Raviart(CR for short) element and the nonconforming enriched Crouzeix-Raviart(ECR for short)…

In this paper, we study the iteration complexity of cubic regularization of Newton method for solving composite minimization problems with uniformly convex objective. We introduce the notion of second-order condition number of a certain…

In this paper, we introduce a unified framework of Tensor Higher-Degree Eigenvalue Complementarity Problem (THDEiCP), which goes beyond the framework of the typical Quadratic Eigenvalue Complementarity Problem (QEiCP) for matrices. First,…

We discuss the (right) eigenvalue equation for $\mathbb{H}$, $\mathbb{C}$ and $\mathbb{R}$ linear quaternionic operators. The possibility to introduce an isomorphism between these operators and real/complex matrices allows to translate the…