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We define and solve classes of sparse matrix problems that arise in multilevel modeling and data analysis. The classes are indexed by the number of nested units, with two-level problems corresponding to the common situation in which data on…
Bi-clustering is a technique that allows for the simultaneous clustering of observations and features in a dataset. This technique is often used in bioinformatics, text mining, and time series analysis. An important advantage of…
We extend a primal-dual fixed point algorithm (PDFP) proposed in [5] to solve two kinds of separable multi-block minimization problems, arising in signal processing and imaging science. This work shows the flexibility of applying PDFP…
In the literature, there exist several studies on symbol-based multigrid methods for the solution of linear systems having structured coefficient matrices. In particular, the convergence analysis for such methods has been obtained in an…
In this paper we focus on the solution of shifted quasiseparable systems and of more general parameter dependent matrix equations with quasiseparable representations. We propose an efficient algorithm exploiting the invariance of the…
We consider fast deterministic algorithms to identify the "best" linearly independent terms in multivariate mixtures and use them to compute, up to a user-selected accuracy, an equivalent representation with fewer terms. One algorithm…
In the present paper, we propose Krylov-based methods for solving large-scale differential Sylvester matrix equations having a low rank constant term. We present two new approaches for solving such differential matrix equations. The first…
Almost block diagonal linear systems of equations can be exemplified by two modules. This makes it possible to construct all sequential forms of band and/or block elimination methods, six old and fourteen new. It allows easy assessment of…
A general stochastic algorithm for solving mixed linear and nonlinear problems was introduced in [11]. We show in this paper how it can be used to solve the fault inverse problem, where a planar fault in elastic half-space and a slip on…
We explore the block nature of the matrix representation of multiplex networks, introducing a new formalism to deal with its spectral properties as a function of the inter-layer coupling parameter. This approach allows us to derive…
The randomized Kaczmarz method is an iterative algorithm that solves overdetermined systems of linear equations. Recently, the method was extended to systems of equalities and inequalities by Leventhal and Lewis. Even more recently, Needell…
Multi-block separable convex problems recently received considerable attention. This class of optimization problems minimizes a separable convex objective function with linear constraints. The algorithmic challenges come from the fact that…
The block diagonal structure of an affinity matrix is a commonly desired property in cluster analysis because it represents clusters of feature vectors by non-zero coefficients that are concentrated in blocks. However, recovering a block…
We develop a novel unified randomized block-coordinate primal-dual algorithm to solve a class of nonsmooth constrained convex optimization problems, which covers different existing variants and model settings from the literature. We prove…
Under consideration are multicomponent minimization problems involving a separable nonsmooth convex function penalizing the components individually, and nonsmooth convex coupling terms penalizing linear mixtures of the components. We…
We present a method for randomizing formulas for bilinear computation of matrix products. We consider the implications of such randomization when there are two sources of error: One due to the formula itself only being approximately…
This paper presents the non-linear generalization of a previous work on matrix differential models. It focusses on the construction of approximate solutions of first-order matrix differential equations Y'(x)=f(x,Y(x)) using matrix-cubic…
Fitting a matrix of a given rank to data in a least squares sense can be done very effectively using 2nd order methods such as Levenberg-Marquardt by explicitly optimizing over a bilinear parameterization of the matrix. In contrast, when…
A numerical approach for solving evolutionary partial differential equations in two and three space dimensions on block-based adaptive grids is presented. The numerical discretization is based on high-order, central finite-differences and…
This paper addresses non-convex constrained optimization problems that are characterized by a scalar complicating constraint. We propose an iterative bisection method for the dual problem (DualBi Algorithm) that recovers a feasible primal…