Search · four archives
Search · four archives
19 papers · ranked by Valyu relevance
Riley Murray, James Demmel, Michael W. Mahoney, N. Benjamin Erichson + 9 more
Randomized numerical linear algebra – RandNLA, for short – concerns the use of randomization as a resource to develop improved algorithms for large-scale linear algebra computations. The origins of contemporary RandNLA lay in theoretical computer science, where it blossomed from a simple idea: randomization provides an…
Per‐Gunnar Martinsson, Joel A. Tropp
Topics include norm estimation; matrix approximation by sampling; structured and unstructured random embeddings; linear regression problems; low-rank approximation; subspace iteration and Krylov methods; error estimation and adaptivity; interpolatory and CUR factorizations; Nystrom approximation of positive…
Petros Drineas, Michael W. Mahoney
| 1 | Introduction | | 2 | | --- | --- | --- | --- | | 2 | Linear Algebra | | 3 | | | 2.1 Basics. | | 3 | | | 2.2 Norms. | | 4 | | | 2.3 Vector norms. | | 4 | | | 2.4 | Induced matrix norms | 5 | | | 2.5 | The Frobenius norm | 6 | | | 2.6 | The Singular Value Decomposition | 7 | | | 2.7 | SVD and Fundamental Matrix…
Michał Dereziński, Michael W. Mahoney
for Machine Learning Authors: ['Michał Dereziński' 'Michael W. Mahoney'] Large matrices arise in many machine learning and data analysis applications, including as representations of datasets, graphs, model weights, and first and second-order derivatives. Randomized Numerical Linear Algebra (RandNLA) is an area which…
Patel, Vivak, Maldonado, D. Adrian + 12 more
This report showcases the role of, and future directions for, the field of Randomized Numerical Linear Algebra (RNLA) in a selection of scientific applications. These applications span the domains of imaging, genomics and dynamical systems, and are thematically connected by needing to perform linear algebra routines on…
Anastasia Kireeva, Joel A. Tropp
This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is illustrated by its application to several computational problems. This treatment…
Meng-Long Xiao, Tao Li, Deanna Needell
The projected linear system solver (PLSS), by incrementally appending columns to a random or deterministic sketching matrix, provides an attractive finite termination property for consistent linear systems. Nevertheless, a critical computational bottleneck of PLSS is accessing the whole coefficient matrix per…
Tim Wallace, Ali Sekmen
Kaczmarz's alternating projection method has been widely used for solving mostly over-determined linear system of equations A x = b in various fields of engineering, medical imaging, and computational science. Because of its simple iterative nature with light computation, this method was successfully applied in…
Haoze He, Daniel Kressner
We present and analyze a simple numerical method that diagonalizes a complex normal matrix A by diagonalizing the Hermitian matrix obtained from a random linear combination of the Hermitian and skew-Hermitian parts of A.
Rishi Advani, Madison Crim, Sean O’Hagan
| 1 | Introduction | | 2 | | --- | --- | --- | --- | | | 1.1 Low-rank Approximation | | 2 | | | 1.2 | Kernel Methods | 2 | | 2 | Johnson-Lindenstrauss Lemma | | 3 | | 3 | Low-rank Approximation | | 6 | | | 3.1 | Singular Value Decomposition | 6 | | | 3.1.1 | Deterministic SVD | 6 | | | 3.1.2 Randomized SVD | | 7 | | |…
Takuya Okuyama, André Röhm, Takatomo Mihana, Makoto Naruse + 1 more
Matrix multiplication is important in various information-processing applications, including the computation of eigenvalues and eigenvectors, and in combinatorial optimization algorithms. Therefore, reducing the computation time of matrix products is essential to speed up scientific and practical calculations. Several…
Zakaria Kasmi, Abdelmoumen Norrdine, Jochen Schiller, Mesut Güneş + 2 more
'Christoph Motzko' 'Raffaele Bruno'] We developped an open source library called RcdMathLib for solving multivariate linear and nonlinear systems. RcdMathLib supports on-the-fly computing on low-cost and resource-constrained devices, e.g., microcontrollers. The decentralized processing is a step towards ubiquitous…
Hanbin Lee, Nathaniel S. Pope, Jerome Kelleher, Gregor Gorjanc + 1 more
Ancestral recombination graphs (ARGs) are an attractive means for quantitative genetic analysis of complex traits because they encode the realized genetic relatedness between a sample of individuals in the presence of genetic drift, recombination, and mutation. Data structures for efficiently storing ARGs can also be…
Gad Abraham, Michael Inouye
Principal component analysis (PCA) is routinely used to analyze genome-wide single-nucleotide polymorphism (SNP) data, for detecting population structure and potential outliers. However, the size of SNP datasets has increased immensely in recent years and PCA of large datasets has become a time consuming task. We have…
Jonathan Oesterle, Nicholas Krämer, Philipp Hennig, Philipp Berens
Understanding neural computation on the mechanistic level requires models of neurons and neuronal networks. To analyze such models one typically has to solve coupled ordinary differential equations (ODEs), which describe the dynamics of the underlying neural system. These ODEs are solved numerically with deterministic…
Pier Paolo Poir, Louis Lagardère, Jean-Philip Piquemal
We propose a new strategy to solve the Tkatchenko-Scheffler Many-Body Dispersion (MBD) model’s equations. Our approach overcomes the original O(N**3) computational complexity that limits its applicability to large molecular systems within thecontext of O(N) Density Functional Theory (DFT). First, in order to generate…
Pier Paolo Poier, Louis Lagardère, Jean-Philip Piquemal
We propose a new strategy to solve the Tkatchenko-Scheffler Many-Body Dispersion (MBD) model’s equations. Our approach overcomes the original O(N**3) computational complexity that limits its applicability to large molecular systems within thecontext of O(N) Density Functional Theory (DFT). First, in order to generate…
Joel T. Martin, Geoffrey M. Boynton, Daniel H. Baker, Alex R. Wade + 1 more
The normal human retina contains several classes of photosensitive cell—rods for low-light vision, three cone classes for daylight vision, and intrinsically photosensitive retinal ganglion cells (ipRGCs) expressing melanopsin for non-image-forming functions including pupil control, melatonin suppression and circadian…
Christian G. Habeck, Adam M. Brickman
Our ability to draw conclusions from experiments often relies on the application of inferential statistics, such as those included within the general-linear-modeling framework. The purpose of this commentary is to direct attention a common fallacy that can be observed in paper reviews and professional exchanges in the…