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This research aims to solve high-dimensional, parameter-dependent elliptic PDEs using low-rank tensor methods.

May 24, 2026Open Access

Low-rank tensor methods for high-dimensional parameter-dependent PDEs: eigenvalue estimation, approximate inverses, and multigrid methods

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This research aims to solve high-dimensional, parameter-dependent elliptic PDEs using low-rank tensor methods.
Develop methods for calculating extremal eigenvalues using a Lanczos-based approach
Create techniques for computing approximate inverses of low-rank tensor operators
Implement a Low-Rank Tensor Toolkit for efficient computations with guarantees.
Efficient estimation of eigenvalues confirmed by numerical experiments using operator applications
Approximate inverses computed with rigorously controlled error bounds
Convergence theory established for the parameter-dependent multigrid method accounting for low-rank truncation.

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Randomized trial develops efficient eigenvalue estimation and multigrid methods in parameter-dependent PDEs, highlighting computational advancements.

Tim Andreas Werthmann (2026) studied this question.

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Randomized trial develops efficient eigenvalue estimation and multigrid methods in parameter-dependent PDEs, highlighting computational advancements.