Related papers: Randomized orthogonalization and Krylov subspace m…
Krylov subspace methods are considered a standard tool to solve large systems of linear algebraic equations in many scientific disciplines such as image restoration or solving partial differential equations in mechanics of continuum. In the…
In this paper we present a novel algorithm developed for computing the QR factorisation of extremely ill-conditioned tall-and-skinny matrices on distributed memory systems. The algorithm is based on the communication-avoiding CholeskyQR2…
We study a version of the randomized Kaczmarz algorithm for solving systems of linear equations where the iterates are confined to the solution space of a selected subsystem. We show that the subspace constraint leads to an accelerated…
This paper introduces new solvers for efficiently computing solutions to large-scale inverse problems with group sparsity regularization, including both non-overlapping and overlapping groups. Group sparsity regularization refers to a type…
In classical frameworks as the Euclidean space, positive definite kernels as well as their analytic properties are explicitly available and can be incorporated directly in kernel-based learning algorithms. This is different if the…
Householder orthogonalization plays an important role in numerical linear algebra. It attains perfect orthogonality regardless of the conditioning of the input. However, in the context of a non-standard inner product, it becomes difficult…
With the growth of model and data sizes, a broad effort has been made to design pruning techniques that reduce the resource demand of deep learning pipelines, while retaining model performance. In order to reduce both inference and training…
This paper addresses the problem of synchronizing orthogonal matrices over directed graphs. For synchronized transformations (or matrices), composite transformations over loops equal the identity. We formulate the synchronization problem as…
A methodology for using random sketching in the context of model order reduction for high-dimensional parameter-dependent systems of equations was introduced in [Balabanov and Nouy 2019, Part I]. Following this framework, we here construct…
Mixed-effects models are widely used to model data with hierarchical grouping structures and high-cardinality categorical predictor variables. However, for high-dimensional crossed random effects, current standard computations relying on…
In this work we present a rational Krylov subspace method for solving real large-scale polynomial eigenvalue problems with T-even (that is, symmetric/skew-symmetric) structure. Our method is based on the Even-IRA algorithm. To preserve the…
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…
Quadratic minimization problems with orthogonality constraints (QMPO) play an important role in many applications of science and engineering. However, some existing methods may suffer from low accuracy or heavy workload for large-scale…
Assessing IC manufacturing process fluctuations and their impacts on IC interconnect performance has become unavoidable for modern DSM designs. However, the construction of parametric interconnect models is often hampered by the rapid…
We address the communication overhead of distributed sparse matrix-(multiple)-vector multiplication in the context of large-scale eigensolvers, using filter diagonalization as an example. The basis of our study is a performance model which…
A square-root-free matrix QR decomposition (QRD) scheme was rederived in [1] based on [2] to simplify computations when solving least-squares (LS) problems on embedded systems. The scheme of [1] aims at eliminating both the square-root and…
Scalable QR factorization algorithms for solving least squares and eigenvalue problems are critical given the increasing parallelism within modern machines. We introduce a more general parallelization of the CholeskyQR2 algorithm and show…
This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of…
This paper deals with the definition and optimization of augmentation spaces for faster convergence of the conjugate gradient method in the resolution of sequences of linear systems. Using advanced convergence results from the literature,…
Krylov subspace methods, such as the Conjugate Gradient (CG) and BiCGSTAB methods, are widely used in scientific computing for solving linear systems. In this study, we propose a new framework for solving large Sylvester equations in a…