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In this article, we establish a class of new projected type iteration methods based on matrix spitting for solving the linear complementarity problem. Also, we provide a sufficient condition for the convergence analysis when the system…
The idea of unfolding iterative algorithms as deep neural networks has been widely applied in solving sparse coding problems, providing both solid theoretical analysis in convergence rate and superior empirical performance. However, for…
In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…
We consider the problem of estimating log-determinants of large, sparse, positive definite matrices. A key focus of our algorithm is to reduce computational cost, and it is based on sparse approximate inverses. The algorithm can be…
We consider a variant of matrix completion where entries are revealed in a biased manner. We wish to understand the extent to which such bias can be exploited in improving predictions. Towards that, we propose a natural model where the…
We consider Gaussian mixture models in high dimensions and concentrate on the twin tasks of detection and feature selection. Under sparsity assumptions on the difference in means, we derive information bounds and establish the performance…
We propose a new method for computing the $\varphi$-functions of large sparse matrices with low rank or fast decaying singular values. The key is to reduce the computation of $\varphi_{\ell}$-functions of a large matrix to…
The growth of big data in domains such as Earth Sciences, Social Networks, Physical Sciences, etc. has lead to an immense need for efficient and scalable linear algebra operations, e.g. Matrix inversion. Existing methods for efficient and…
We provide tools to help automate the error analysis of algorithms that evaluate simple functions over the floating-point numbers. The aim is to obtain tight relative error bounds for these algorithms, expressed as a function of the unit…
This paper considers the design of tunable decision schemes capable of rejecting with high probability mismatched signals embedded in Gaussian interference with unknown covariance matrix. To this end, a sparse recovery technique is…
We provide another framework of iterative algorithms based on thresholding, feedback and null space tuning for sparse signal recovery arising in sparse representations and compressed sensing. Several thresholding algorithms with various…
This paper extends the framework of randomised matrix multiplication to a coarser partition and proposes an algorithm as a complement to the classical algorithm, especially when the optimal probability distribution of the latter one is…
We study the performance of sparse regression methods and propose new techniques to distill the governing equations of dynamical systems from data. We first look at the generic methodology of learning interpretable equation forms from data,…
Second-order optimization methods have desirable convergence properties. However, the exact Newton method requires expensive computation for the Hessian and its inverse. In this paper, we propose SPAN, a novel approximate and fast Newton…
Limited by fixed step-size and sparsity penalty factor, the conventional sparsity-aware normalized subband adaptive filtering (NSAF) type algorithms suffer from trade-off requirements of high filtering accurateness and quicker convergence…
Sparsity-constrained optimization underlies many problems in signal processing, statistics, and machine learning. State-of-the-art hard-thresholding (HT) algorithms rely on an appropriately selected continuous step-size parameter to ensure…
In this article, we study algorithms for nonnegative matrix factorization (NMF) in various applications involving streaming data. Utilizing the continual nature of the data, we develop a fast two-stage algorithm for highly efficient and…
Recent technological developments have led to big data processing, which resulted in significant computational difficulties when solving large-scale linear systems or inverting matrices. As a result, fast approximate iterative matrix…
We propose a new technique for adaptive identification of sparse systems based on the compressed sensing (CS) theory. We manipulate the transmitted pilot (input signal) and the received signal such that the weights of adaptive filter…
In this paper, we aim to compute numerical approximation integral by using an adaptive Monte Carlo algorithm. We propose a stratified sampling algorithm based on an iterative method which splits the strata following some quantities called…