Abstract
In this paper we propose an efficient algorithm to compute low-rank approximation to the solution of so-called “Laplace-like” linear systems. The idea is to transform the problem into the frequency domain, and then use cross approximation. In this case, we do not need to form explicit approximation to the inverse operator, and can approximate the solution directly, which leads to reduced complexity. We demonstrate that our method is fast and robust by using it as a solver inside Uzawa iterative method for solving the Stokes problem.
Funding source: Russian Foundation for Basic Research
Award Identifier / Grant number: 16-31-60095
Funding statement: This work was supported by the Russian Foundation for Basic Research, grant 16-31-60095.
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- 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
Artikel in diesem Heft
- 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