相关论文: Deviation Maximization for Rank-Revealing QR Facto…

The problem of decomposing a given covariance matrix as the sum of a positive semi-definite matrix of given rank and a positive semi-definite diagonal matrix, is considered. We present a projection-type algorithm to address this problem.…

This article proposes and analyzes several variants of the randomized Cholesky QR factorization of a matrix $X$. Instead of computing the R factor from $X^T X$, as is done by standard methods, we obtain it from a small, efficiently…

In this paper, a reduced-rank scheme with joint iterative optimization is presented for direction of arrival estimation. A rank-reduction matrix and an auxiliary reduced-rank parameter vector are jointly optimized to calculate the output…

Matrix decomposition is a very important mathematical tool in numerical linear algebra for data processing. In this paper, we introduce a new randomized matrix decomposition algorithm, which is called randomized approximate SVD based on…

Reinforcement learning (RL) in episodic, factored Markov decision processes (FMDPs) is studied. We propose an algorithm called FMDP-BF, which leverages the factorization structure of FMDP. The regret of FMDP-BF is shown to be exponentially…

The QLP decomposition is one of the effective algorithms to approximate singular value decomposition (SVD) in numerical linear algebra. In this paper, we propose some single-pass randomized QLP decomposition algorithms for computing the…

Transforming a matrix over a field to echelon form, or decomposing the matrix as a product of structured matrices that reveal the rank profile, is a fundamental building block of computational exact linear algebra. This paper surveys the…

We propose an algorithm for solving nonlinear convex programs defined in terms of a symmetric positive semidefinite matrix variable $X$. This algorithm rests on the factorization $X=Y Y^T$, where the number of columns of Y fixes the rank of…

We consider exact matrix decomposition by Gauss-Bareiss reduction. We investigate two aspects of the process: common row and column factors and the influence of pivoting strategies. We identify two types of common factors: systematic and…

In this work we apply the "deviation maximization", a new column selection strategy, to the Lawson-Hanson algorithm for the solution of NonNegative Least Squares (NNLS), devising a new algorithm we call Lawson-Hanson with Deviation…

This paper examines the nonconvex quadratically constrained quadratic programming (QCQP) problems using an iterative method. One of the existing approaches for solving nonconvex QCQP problems relaxes the rank one constraint on the unknown…

A QR factorization of a tall and skinny matrix with n columns can be represented as a reduction. The operation used along the reduction tree has in input two n-by-n upper triangular matrices and in output an n-by-n upper triangular matrix…

Standard Markov decision process (MDP) and reinforcement learning algorithms optimize the policy with respect to the expected gain. We propose an algorithm which enables to optimize an alternative objective: the probability that the gain is…

The Nystr\"om method is a convenient heuristic method to obtain low-rank approximations to kernel matrices in nearly linear complexity. Existing studies typically use the method to approximate positive semidefinite matrices with low or…

We present two new algorithms for Householder QR factorization of Block Low-Rank (BLR) matrices: one that performs block-column-wise QR, and another that is based on tiled QR. We show how the block-column-wise algorithm exploits BLR…

In the context of solving large distributed constraint optimization problems (DCOP), belief-propagation and approximate inference algorithms are candidates of choice. However, in general, when the factor graph is very loopy (i.e. cyclic),…

As multicore systems continue to gain ground in the High Performance Computing world, linear algebra algorithms have to be reformulated or new algorithms have to be developed in order to take advantage of the architectural features on these…

We study the problem of estimating the optimal Q-function of $\gamma$-discounted Markov decision processes (MDPs) under the synchronous setting, where independent samples for all state-action pairs are drawn from a generative model at each…

Recently, Information Retrieval community has witnessed fast-paced advances in Dense Retrieval (DR), which performs first-stage retrieval with embedding-based search. Despite the impressive ranking performance, previous studies usually…

We consider the problem of computing a QR (or QZ) decomposition of a real, dense, tall and very skinny matrix. That is, the number of columns is tiny compared to the number of rows, rendering most computations completely or partially…