Iterative refinement of Schur decompositions

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a suitable Krylov ...

A key challenge across many disciplines is to extract meaningful information from data which is often obscured by noise. These datasets are typically represented as large matrices. Given the current trend of ever-increasing data volumes, with datasets grow ...

Negative triangularity (NT) scenarios in TCV have been compared to positive triangularity (PT) scenarios using the same plasma shapes foreseen for divertor tokamak test tokamak operations. The experiments provided a NT/PT L-mode pair and a PT H-mode with d ...

Given a family of nearly commuting symmetric matrices, we consider the task of computing an orthogonal matrix that nearly diagonalizes every matrix in the family. In this paper, we propose and analyze randomized joint diagonalization (RJD) for performing t ...

Spectral algorithms are some of the main tools in optimization and inference problems on graphs. Typically, the graph is encoded as a matrix and eigenvectors and eigenvalues of the matrix are then used to solve the given graph problem. Spectral algorithms ...

The increasing complexity of transformer models in artificial intelligence expands their computational costs, memory usage, and energy consumption. Hardware acceleration tackles the ensuing challenges by designing processors and accelerators tailored for t ...

In this work, we study the impact of aspect ratio A = R 0 / r (the ratio of major radius R 0 to minor radius r) on the confinement benefits of negative triangularity (NT) plasma shaping. We use high-fidelity flux tube gyrokinetic GENE simulations and consi ...

Materials for high -temperature environments are actively being investigated for deployment in aerospace and nuclear applications. This study uses computational approaches to unravel the crystallography and thermodynamics of a promising class of refractory ...

The desire and ability to place AI-enabled applications on the edge has grown significantly in recent years. However, the compute-, area-, and power-constrained nature of edge devices are stressed by the needs of the AI-enabled applications, due to a gener ...

Experimental measurements of the turbulence amplitude utilizing a short pulse reflectometry method are presented. Two discharges with shaped plasma possessing opposite signs of triangularity are considered and a higher turbulence amplitude is found in the ...

Ashenhurst-Curtis decomposition (ACD) is a decomposition technique used, in particular, to map combinational logic into lookup tables (LUTs) structures when synthesizing hardware designs. However, available implementations of ACD suffer from excessive comp ...

Carbon impurity transport is studied in the TCV tokamak using a charge exchange recombination diagnostic. TCVs flexible shaping capabilities were exploited to extend previous impurity transport studies to negative triangularity (delta < 0). A practical way ...

Plasmas with negative triangularity (NT) shape have been recently shown to be able to achieve H-mode levels of confinement in L-mode, avoiding detrimental edge localised modes. Therefore, this plasma geometry is now studied as a possible viable option for ...

The SMall Aspect Ratio Tokamak (SMART) under commissioning at the University of Seville, Spain, aims to explore confinement properties and possible advantages in confinement for compact/spherical tokamaks operating at negative vs. positive triangularity. T ...

In this thesis we will present and analyze randomized algorithms for numerical linear algebra problems. An important theme in this thesis is randomized low-rank approximation. In particular, we will study randomized low-rank approximation of matrix functio ...

For a high-dimensional problem, a randomized Gram-Schmidt (RGS) algorithm is beneficial in terms of both computational cost and numerical stability. We apply this dimension reduction technique by random sketching to Krylov subspace methods, e.g., to the ge ...

This paper studies kernel ridge regression in high dimensions under covariate shifts and analyzes the role of importance re-weighting. We first derive the asymptotic expansion of high dimensional kernels under covariate shifts. By a bias-variance decomposi ...

Sylvester matrix equations are ubiquitous in scientific computing. However, few solution techniques exist for their generalized multiterm version, as they now arise in an increasingly large number of applications. In this work, we consider algebraic parame ...

State-of-the-art Artificial Intelligence (AI) algorithms, such as graph neural networks and recommendation systems, require floating-point computation of very large matrix multiplications over sparse data. Their execution in resource-constrained scenarios, ...

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, we propose a mix ...

Iterative refinement of Schur decompositions

Chat with Graph Search

SPEEDING UP KRYLOV SUBSPACE METHODS FOR COMPUTING f(A)b VIA RANDOMIZATION

Spectral Estimators for High-Dimensional Matrix Inference

Experiments and gyrokinetic simulations of TCV plasmas with negative triangularity in view of DTT operations

RANDOMIZED JOINT DIAGONALIZATION OF SYMMETRIC

The Power of Two Matrices in Spectral Algorithms for Community Recovery

Accelerator-driven Data Arrangement to Minimize Transformers Run-time on Multi-core Architectures

Physical insights from the aspect ratio dependence of turbulence in negative triangularity plasmas

First-principles thermodynamics of precipitation in aluminum-containing refractory alloys

Exploring High-Performance and Energy-Efficient Architectures for Edge AI-Enabled Applications

Validation of short-pulse reflectometry turbulence measurements with a synthetic diagnostic

Enhancing Delay-Driven LUT Mapping with Boolean Decomposition

Study of impurity C transport and plasma rotation in negative triangularity on the TCV tokamak

First-principle based predictions of the effects of negative triangularity on DTT scenarios

NBI optimization on SMART and implications for scenario development

Randomized low-rank approximation and its applications

Randomized flexible GMRES with deflated restarting

High-Dimensional Kernel Methods under Covariate Shift: Data-Dependent Implicit Regularization

Preconditioning techniques for generalized Sylvester matrix equations

A 16-bit Floating-Point Near-SRAM Architecture for Low-power Sparse Matrix-Vector Multiplication

A mixed precision LOBPCG algorithm