Related papers: Accelerating the Computation of Tensor $Z$-eigenva…
The performance of numerical micromagnetic models is limited by the demagnetizing field computation, which typically accounts for the majority of the computation time. For magnetization dynamics simulations explicit evaluation methods are…
Randomized numerical linear algebra is proved to bridge theoretical advancements to offer scalable solutions for approximating tensor decomposition. This paper introduces fast randomized algorithms for solving the fixed Tucker-rank problem…
Let $n$ be a positive integer and $m$ be a positive even integer. Let ${\mathcal A}$ be an $m^{th}$ order $n$-dimensional real weakly symmetric tensor and ${\mathcal B}$ be a real weakly symmetric positive definite tensor of the same size.…
In this paper, the Newton-Anderson method, which results from applying an extrapolation technique known as Anderson acceleration to Newton's method, is shown both analytically and numerically to provide superlinear convergence to non-simple…
We consider two high-order tuners that have been shown to have accelerated performance, one based on Polyak's heavy ball method and another based on Nesterov's acceleration method. We show that parameter estimates are bounded and converge…
We introduce the concept of mode-k generalized eigenvalues and eigenvectors of a tensor and prove some properties of such eigenpairs. In particular, we derive an upper bound for the number of equivalence classes of generalized tensor…
The purpose of this paper is to study the problem of computing unitary eigenvalues (U-eigenvalues) of non-symmetric complex tensors. By means of symmetric embedding of complex tensors, the relationship between U-eigenpairs of a…
We show that Nesterov acceleration is an optimal-order iterative regularization method for linear ill-posed problems provided that a parameter is chosen accordingly to the smoothness of the solution. This result is proven both for an a…
The aim of this paper is to propose an efficient adaptive finite element method for eigenvalue problems based on the multilevel correction scheme and inverse power method. This method involves solving associated boundary value problems on…
We present a novel approach for accelerating AI performance by leveraging Anderson extrapolation, a vector-to-vector mapping technique based on a window of historical iterations. By identifying the crossover point (Fig. 1) where a mixing…
In this paper, we derive an asymptotic error expansion for the eigenvalue approximations by the lowest order Raviart-Thomas mixed finite element method for the general second order elliptic eigenvalue problems. Extrapolation based on such…
This paper proposes an accelerated proximal point method for maximally monotone operators. The proof is computer-assisted via the performance estimation problem approach. The proximal point method includes various well-known convex…
Aitken extrapolation normally applied to convergent fixed point iteration is extended to extrapolate the solution of a divergent iteration. In addition, higher order Aitken extrapolation is introduced that enables successive decomposition…
Extrapolation is a well-known technique for solving convex optimization and variational inequalities and recently attracts some attention for non-convex optimization. Several recent works have empirically shown its success in some machine…
Function approximation from input and output data is one of the most investigated problems in signal processing. This problem has been tackled with various signal processing and machine learning methods. Although tensors have a rich history…
In this paper we accomplish the development of the fast rank-adaptive solver for tensor-structured symmetric positive definite linear systems in higher dimensions. In [arXiv:1301.6068] this problem is approached by alternating minimization…
We describe convergence acceleration schemes for multistep optimization algorithms. The extrapolated solution is written as a nonlinear average of the iterates produced by the original optimization method. Our analysis does not need the…
This paper examines a number of extrapolation and acceleration methods, and introduces a few modifications of the standard Shanks transformation that deal with general sequences. One of the goals of the paper is to lay out a general…
Finding the maximum eigenvalue of a symmetric tensor is an important topic in tensor computation and numerical multilinear algebra. This paper is devoted to a semi-definite program algorithm for computing the maximum $H$-eigenvalue of a…
We develop algebraic methods for computations with tensor data. We give 3 applications: extracting features that are invariant under the orthogonal symmetries in each of the modes, approximation of the tensor spectral norm, and…