Related papers: Local, Smooth, and Consistent Jacobi Set Simplific…

Jacobi's method is a well-known algorithm in linear algebra to diagonalize symmetric matrices by successive elementary rotations. We report about the generalization of these elementary rotations towards canonical transformations acting in…

In this paper we introduce an iterative Jacobi algorithm for solving distributed model predictive control (DMPC) problems, with linear coupled dynamics and convex coupled constraints. The algorithm guarantees stability and persistent…

Using a change of basis in the algebra of symmetric functions, we compute the moments of the Hermitian Jacobi process. After a careful arrangement of the terms and the evaluation of the determinant of an `almost upper-triangular' matrix, we…

Many problems give rise to polynomial systems. These systems often have several parameters and we are interested to study how the solutions vary when we change the values for the parameters. Using predictor-corrector methods we track the…

In this paper we prove the global convergence of the complex Jacobi method for Hermitian matrices for a large class of generalized serial pivot strategies. For a given Hermitian matrix $A$ of order $n$ we find a constant $\gamma<1$…

The goal of this paper is to study approaches to bridge the gap between first-order and second-order type methods for composite convex programs. Our key observations are: i) Many well-known operator splitting methods, such as…

We address the computational spectral theory of Jacobi operators that are compact perturbations of the free Jacobi operator via the asymptotic properties of a connection coefficient matrix. In particular, for finite-rank perturbation we…

The discrete spectrum of complex Jacobi matrices that are compact perturbations of the discrete laplacian is under consideration. The rate of stabilization for the the matrix entries which provides finiteness of the discrete spectrum and is…

We present an efficient algorithm for least-squares constrained nuclear norm minimization, a computationally challenging problem with broad applications. Our approach combines a level set method with secant iterations and a proximal…

We present an algorithm which produces a decomposition of a regular cellular complex with a discrete Morse function analogous to the Morse-Smale decomposition of a smooth manifold with respect to a smooth Morse function. The advantage of…

Each iteration in Jacobi-Davidson method for solving large sparse eigenvalue problems involves two phases, called subspace expansion and eigen pair extraction. The subspace expansion phase involves solving a correction equation. We propose…

We present local biplots, a an extension of the classic principal components biplot to multi-dimensional scaling. Noticing that principal components biplots have an interpretation as the Jacobian of a map from data space to the principal…

Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…

In this paper it is shown that the space of tight geodesic segments connecting any two vertices in a complex of cycles has finite, uniformly bounded dimension. The dimension is defined in terms of a discrete analogue of Jacobi fields, which…

Discrete Morse theory helps us compute the homology groups of simplicial complexes in an efficient manner. A "good" gradient vector field reduces the number of critical simplices, simplifying the homology calculations by reducing them to…

In this paper, we consider a family of Jacobi-type algorithms for simultaneous orthogonal diagonalization problem of symmetric tensors. For the Jacobi-based algorithm of [SIAM J. Matrix Anal. Appl., 2(34):651--672, 2013], we prove its…

In this paper, we study the Jacobi frame approximation with equispaced samples and derive an error estimation. We observe numerically that the approximation accuracy gradually decreases as the extended domain parameter $\gamma$ increases in…

We set out to build a framework for self-adjoint extension theory for powers of the Jacobi differential operator that does not make use of classical deficiency elements. Instead, we rely on simpler functions that capture the impact of these…

We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…

We consider the problem of minimizing a smooth, Lipschitz, convex function over a compact, convex set using sub-zeroth-order oracles: an oracle that outputs the sign of the directional derivative for a given point and a given direction, an…