Related papers: Using Mixed Precision in Low-Synchronization Reort…
The modified Gram-Schmidt (MGS) orthogonalization is one of the most well-used algorithms for computing the thin QR factorization. MGS can be straightforwardly extended to a non-standard inner product with respect to a symmetric positive…
The locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm is a popular approach for computing a few smallest eigenvalues and the corresponding eigenvectors of a large Hermitian positive definite matrix A. In this work,…
The parallel strong-scaling of Krylov iterative methods is largely determined by the number of global reductions required at each iteration. The GMRES and Krylov-Schur algorithms employ the Arnoldi algorithm for nonsymmetric matrices. The…
In this paper, based on the limited memory techniques and subspace minimization conjugate gradient (SMCG) methods, a regularized limited memory subspace minimization conjugate gradient method is proposed, which contains two types of…
The use of reduced and mixed precision computing has gained increasing attention in high-performance computing (HPC) as a means to improve computational efficiency, particularly on modern hardware architectures like GPUs. In this work, we…
State-of-the-art algorithms for sparse subspace clustering perform spectral clustering on a similarity matrix typically obtained by representing each data point as a sparse combination of other points using either basis pursuit (BP) or…
Linear systems in applications are typically well-posed, and yet the coefficient matrices may be nearly singular in that the condition number $\kappa(\boldsymbol{A})$ may be close to $1/\varepsilon_{w}$, where $\varepsilon_{w}$ denotes the…
Block Gram-Schmidt algorithms serve as essential kernels in many scientific computing applications, but for many commonly used variants, a rigorous treatment of their stability properties remains open. This work provides a comprehensive…
Renewed interest in mixed-precision algorithms has emerged due to growing data capacity and bandwidth concerns, as well as the advancement of GPUs, which enable significant speedup for low precision arithmetic. In light of this, we propose…
High order exponential integrators require computing linear combination of exponential like $\varphi$-functions of large matrices $A$ times a vector $v$. Krylov projection methods are the most general and remain an efficient choice for…
Low complexity joint estimation of synchronization impairments and channel in a single-user MIMO-OFDM system is presented in this letter. Based on a system model that takes into account the effects of synchronization impairments such as…
With the emergence of mixed precision capabilities in hardware, iterative refinement schemes for solving linear systems $Ax=b$ have recently been revisited and reanalyzed in the context of three or more precisions. These new analyses show…
Sketching-based preconditioners have been shown to accelerate the solution of dense least-squares problems with coefficient matrices having substantially more rows than columns. The cost of generating these preconditioners can be reduced by…
Saddle point problems arise in many important practical applications. In this paper we propose and analyze some algorithms for solving symmetric saddle point problems which are based upon the block Gram-Schmidt method. In particular, we…
A framework based on iterative coordinate minimization (CM) is developed for stochastic convex optimization. Given that exact coordinate minimization is impossible due to the unknown stochastic nature of the objective function, the crux of…
We revisit the source image estimation problem from blind source separation (BSS). We generalize the traditional minimum distortion principle to maximum likelihood estimation with a model for the residual spectrograms. Because residual…
The classic method for computing the spectral decomposition of a real symmetric matrix, the Jacobi algorithm, can be accelerated by using mixed precision arithmetic. The Jacobi algorithm is aiming to reduce the off-diagonal entries…
In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…
A new inverse iteration algorithm that can be used to compute all the eigenvectors of a real symmetric tri-diagonal matrix on parallel computers is developed. The modified Gram-Schmidt orthogonalization is used in the classical inverse…
One of the limitations of recycled GCRO methods is the large amount of computation required to orthogonalize the basis vectors of the newly generated Krylov subspace for the approximate solution when combined with those of the recycle…