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Sparse polynomial chaos expansions: Literature survey and benchmark
Sparse polynomial chaos expansions (PCE) are a popular surrogate modelling method that
takes advantage of the properties of PCE, the sparsity-of-effects principle, and powerful …
takes advantage of the properties of PCE, the sparsity-of-effects principle, and powerful …
Randomized numerical linear algebra: Foundations and algorithms
PG Martinsson, JA Tropp - Acta Numerica, 2020 - cambridge.org
This survey describes probabilistic algorithms for linear algebraic computations, such as
factorizing matrices and solving linear systems. It focuses on techniques that have a proven …
factorizing matrices and solving linear systems. It focuses on techniques that have a proven …
[كتاب][B] An invitation to compressive sensing
This first chapter formulates the objectives of compressive sensing. It introduces the
standard compressive problem studied throughout the book and reveals its ubiquity in many …
standard compressive problem studied throughout the book and reveals its ubiquity in many …
Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm
We improve a recent gurantee of Bach and Moulines on the linear convergence of SGD for
smooth and strongly convex objectives, reducing a quadratic dependence on the strong …
smooth and strongly convex objectives, reducing a quadratic dependence on the strong …
Compressive sensing and structured random matrices
H Rauhut - Theoretical foundations and numerical methods for …, 2010 - degruyter.com
These notes give a mathematical introduction to compressive sensing focusing on recovery
using1-minimization and structured random matrices. An emphasis is put on techniques for …
using1-minimization and structured random matrices. An emphasis is put on techniques for …
[كتاب][B] Numerical fourier analysis
The Applied and Numerical Harmonic Analysis (ANHA) book series aims to provide the
engineering, mathematical, and scientific communities with significant developments in …
engineering, mathematical, and scientific communities with significant developments in …
A non-adapted sparse approximation of PDEs with stochastic inputs
We propose a method for the approximation of solutions of PDEs with stochastic coefficients
based on the direct, ie, non-adapted, sampling of solutions. This sampling can be done by …
based on the direct, ie, non-adapted, sampling of solutions. This sampling can be done by …
Extracting sparse high-dimensional dynamics from limited data
H Schaeffer, G Tran, R Ward - SIAM Journal on Applied Mathematics, 2018 - SIAM
Extracting governing equations from dynamic data is an essential task in model selection
and parameter estimation. The form of the governing equation is rarely known a priori; …
and parameter estimation. The form of the governing equation is rarely known a priori; …
Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies
Sampling orthogonal polynomial bases via Monte Carlo is of interest for uncertainty
quantification of models with random inputs, using Polynomial Chaos (PC) expansions. It is …
quantification of models with random inputs, using Polynomial Chaos (PC) expansions. It is …
Exact recovery of chaotic systems from highly corrupted data
Learning the governing equations in dynamical systems from time-varying measurements is
of great interest across different scientific fields. This task becomes prohibitive when such …
of great interest across different scientific fields. This task becomes prohibitive when such …