Numerical Linear Algebra with Applications· 2012Q1
A projection method to solve linear systems in tensor format
- 209citations
- Q1SCImago
- 2012year
Short summary
A novel iterative projection method solves linear systems in low-rank tensor format, enabling computations for high-dimensional problems like discretized PDEs.
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Key points
- Proposes an iterative projection method for linear systems in low-rank tensor format.
- Projects the residual onto a low-dimensional subspace derived from matrix-residual applications.
- Utilizes hierarchical Tucker format for high-dimensional computations.
- Employs a multilevel method to handle mode size dependency.
- Demonstrates effectiveness on high-dimensional convection-diffusion equations.
AI-generated from the title and abstract; the full text is not read.
Abstract
SUMMARY In this paper, we propose a method for the numerical solution of linear systems of equations in low rank tensor format. Such systems may arise from the discretisation of PDEs in high dimensions, but our method is not limited to this type of application. We present an iterative scheme, which is based on the projection of the residual to a low dimensional subspace. The subspace is spanned by vectors in low rank tensor format which—similarly to Krylov subspace methods—stem from the subsequent (approximate) application of the given matrix to the residual. All calculations are performed in hierarchical Tucker format, which allows for applications in high dimensions. The mode size dependency is treated by a multilevel method. We present numerical examples that include high‐dimensional convection–diffusion equations.Copyright © 2012 John Wiley & Sons, Ltd.
The authors' abstract, as published at the source. Numerical Linear Algebra with Applications, 2012 · DOI ↗
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Field: Computational Mathematics
Computational MathematicsMathematics