Abstract
This paper aims at the efficient numerical solution of stochastic eigenvalue problems. Such problems often lead to prohibitively high-dimensional systems with tensor product structure when discretized with the stochastic Galerkin method. Here, we exploit this inherent tensor product structure to develop a globalized low-rank inexact Newton method with which we tackle the stochastic eigenproblem. We illustrate the effectiveness of our solver with numerical experiments.
Funding statement: The work was performed while Martin Stoll was at the Max Planck Institute for Dynamics of Complex Technical Systems.
References
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Tensor Numerical Methods: Actual Theory and Recent Applications
- A Low-Rank Inexact Newton–Krylov Method for Stochastic Eigenvalue Problems
- A Tensor Decomposition Algorithm for Large ODEs with Conservation Laws
- Non-intrusive Tensor Reconstruction for High-Dimensional Random PDEs
- Quasi-Optimal Rank-Structured Approximation to Multidimensional Parabolic Problems by Cayley Transform and Chebyshev Interpolation
- Projection Methods for Dynamical Low-Rank Approximation of High-Dimensional Problems
- Tensor Train Spectral Method for Learning of Hidden Markov Models (HMM)
- Tucker Tensor Analysis of Matérn Functions in Spatial Statistics
- Low-Rank Space-Time Decoupled Isogeometric Analysis for Parabolic Problems with Varying Coefficients
- Approximate Solution of Linear Systems with Laplace-like Operators via Cross Approximation in the Frequency Domain
- Rayleigh Quotient Methods for Estimating Common Roots of Noisy Univariate Polynomials
Articles in the same Issue
- Frontmatter
- Tensor Numerical Methods: Actual Theory and Recent Applications
- A Low-Rank Inexact Newton–Krylov Method for Stochastic Eigenvalue Problems
- A Tensor Decomposition Algorithm for Large ODEs with Conservation Laws
- Non-intrusive Tensor Reconstruction for High-Dimensional Random PDEs
- Quasi-Optimal Rank-Structured Approximation to Multidimensional Parabolic Problems by Cayley Transform and Chebyshev Interpolation
- Projection Methods for Dynamical Low-Rank Approximation of High-Dimensional Problems
- Tensor Train Spectral Method for Learning of Hidden Markov Models (HMM)
- Tucker Tensor Analysis of Matérn Functions in Spatial Statistics
- Low-Rank Space-Time Decoupled Isogeometric Analysis for Parabolic Problems with Varying Coefficients
- Approximate Solution of Linear Systems with Laplace-like Operators via Cross Approximation in the Frequency Domain
- Rayleigh Quotient Methods for Estimating Common Roots of Noisy Univariate Polynomials