Related papers: A hierarchically blocked Jacobi SVD algorithm for …
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…
The eigenvalue problem is a fundamental problem in scientific computing. In this paper, we first give the error analysis for a single step or sweep of Jacobi's method in floating point arithmetic. Then we propose a mixed precision…
In light of today's massive data processing, digital computers are reaching fundamental performance limits due to physical limitations and energy consumption. For specific applications, tailored analog systems offer promising alternatives…
Singular Value Decomposition (SVD) is a powerful tool for multivariate analysis. However, independent computation of the SVD for each sample taken from a bandlimited matrix random process will result in singular value sample paths whose…
Due to importance of reducing of time solution in numerical codes, we propose an algorithm for parallel LU decomposition solver for dense and sparse matrices on GPU. This algorithm is based on first bi-vectorizing a triangular matrices of…
The paper presents a strategy to construct an incremental Singular Value Decomposition (SVD) for time-evolving, spatially 3D discrete data sets. A low memory access procedure for reducing and deploying the snapshot data is presented.…
Asynchronous tasks, when created with over-decomposition, enable automatic computation-communication overlap which can substantially improve performance and scalability. This is not only applicable to traditional CPU-based systems, but also…
In this work, we propose an efficient adaptive multilevel preconditioned Jacobi-Davidson (PJD) method for eigenvalue problems with singularity. Our multilevel method utilizes a local smoothing strategy to solve the preconditioned…
We demonstrate a novel technique to obtain singular-value decomposition (SVD) of the coupled-cluster triple excitations amplitudes, $t_{ijk}^{abc}$. The presented method is based on the Golub-Kahan bidiagonalisation strategy and does not…
The incremental singular value decomposition (SVD) updates a truncated SVD as new columns arrive, replacing a single large SVD with a sequence of small ones. In floating-point arithmetic, each update multiplies the running singular basis by…
Speculative Jacobi Decoding (SJD) has emerged as a promising method for accelerating autoregressive image generation. Despite its potential, existing SJD approaches often suffer from the low acceptance rate issue of speculative tokens due…
An algorithm is developed to compute the complete CS decomposition (CSD) of a partitioned unitary matrix. Although the existence of the CSD has been recognized since 1977, prior algorithms compute only a reduced version (the 2-by-1 CSD)…
The singular value decomposition (SVD) is not only a classical theory in matrix computation and analysis, but also is a powerful tool in machine learning and modern data analysis. In this tutorial we first study the basic notion of SVD and…
We evaluate performance of associative memory in a neural network by based on the singular value decomposition (SVD) of image data stored in the network. We consider the situation in which the original image and its highly coarse-grained…
Large graphs commonly appear in social networks, knowledge graphs, recommender systems, life sciences, and decision making problems. Summarizing large graphs by their high level properties is helpful in solving problems in these settings.…
Variables in many massive high-dimensional data sets are structured, arising for example from measurements on a regular grid as in imaging and time series or from spatial-temporal measurements as in climate studies. Classical multivariate…
We describe and analyze a simple algorithm for principal component analysis and singular value decomposition, VR-PCA, which uses computationally cheap stochastic iterations, yet converges exponentially fast to the optimal solution. In…
We propose new iterative methods for computing nontrivial extremal generalized singular values and vectors. The first method is a generalized Davidson-type algorithm and the second method employs a multidirectional subspace expansion…
A Cross-Product Free (CPF) Jacobi-Davidson (JD) type method is proposed to compute a partial generalized singular value decomposition (GSVD) of a large regular matrix pair $(A,B)$. It implicitly solves the mathematically equivalent…
This article studies the problem of decentralized Singular Value Decomposition (d-SVD), which is fundamental in various signal processing applications. Two scenarios are considered depending on the availability of the data matrix under…