Simons Workshop — Linear Systems and Eigenvalue Problems
All 47 numbered problems in version 3 indexed. Two benchmark-design directions are selected; numbered pointers alone do not certify current openness. Read the source updates for later solutions.
47 catalogue entries · 2 new problem records · 2 catalogue entries linked to problem records
Catalogue entries can be source pointers, solved items or groups of questions. They are not added to the main problem count. Status reflects the saved source, inspected 2026-09-10.
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47 matching entries
Clear filtersReproducible parameterized linear-system benchmarks
Status unassessedSelected source questions
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Algorithms for analyzable linear-system benchmark families
Status unassessedSelected source questions
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 2.3
Status unassessed2.2 Correctness of multigrid methods beyond the standard model problems
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 2.4
Status unassessed2.3 Conjugate gradient versus sketch-and-project
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 2.5
Status unassessed2.4 The effect of outlying singular values (or eigenvalues)
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 2.6
Status unassessed2.4 The effect of outlying singular values (or eigenvalues)
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 2.7
Status unassessed2.4 The effect of outlying singular values (or eigenvalues)
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 2.8
Status unassessed2.4 The effect of outlying singular values (or eigenvalues)
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 2.9
Status unassessed2.4 The effect of outlying singular values (or eigenvalues)
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 2.10
Status unassessed2.4 The effect of outlying singular values (or eigenvalues)
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 2.11
Status unassessed2.5 Preconditioning and convergence of iterative solvers
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 2.12
Status unassessed2.5 Preconditioning and convergence of iterative solvers
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 2.13
Status unassessed2.5 Preconditioning and convergence of iterative solvers
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 2.14
Status unassessed2.5 Preconditioning and convergence of iterative solvers
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 2.15
Status unassessed2.6 Symmetric Krylov methods in finite precision arithmetic
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 2.16
Status unassessed2.6 Symmetric Krylov methods in finite precision arithmetic
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 2.17
Status unassessed2.6 Symmetric Krylov methods in finite precision arithmetic
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 2.18
Status unassessed2.6 Symmetric Krylov methods in finite precision arithmetic
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 2.19
Status unassessed2.6 Symmetric Krylov methods in finite precision arithmetic
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 2.20
Status unassessed2.7 The Forsythe conjecture
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 3.1
Status unassessed3.1 Deterministic pseudospectral shattering / Minami bound
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 3.2
Status unassessedRemarks.
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 3.3
Status unassessed3.2 Accuracy vs. precision in efficient diagonalization algorithms
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 3.4
Status unassessed3.3 Ritz values and approximate invariant subspaces
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 3.5
Status unassessed3.3 Ritz values and approximate invariant subspaces
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 3.6
Status unassessed3.3 Ritz values and approximate invariant subspaces
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 3.7
Status unassessed3.4 Revisiting 𝐌𝐑 𝟑 {\rm MR}^{3}
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 3.8
Status unassessed3.4 Revisiting 𝐌𝐑 𝟑 {\rm MR}^{3}
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 3.9
Status unassessed3.5 Largest / rightmost eigenvalue
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 4.1
Status unassessed4.1 When do greedy/randomized column selection algorithms work?
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 4.2
Status unassessed4.1.1 The discrete Lehmann representation
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 4.3
Status unassessed4.1.2 Orthogonal rows
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 4.4
Status unassessed4.1.3 Incoherence and random row subsampling
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 4.5
Status unassessed4.1.4 Block-column subset selection for rank-structured matrices
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 4.6
Status unassessed4.1.5 Inverses of Laplacians and related matrices
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 4.7
Status unassessed4.2 Clarifying relations between volume sampling and optimal subset selection
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 5.1
Status unassessed5.1 Injections vs. embeddings
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 5.2
Status unassessed5.1 Injections vs. embeddings
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 5.3
Status unassessed5.1 Injections vs. embeddings
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 5.4
Status unassessed5.2 Sparse dimensionality reduction maps
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 5.5
Status unassessed5.2 Sparse dimensionality reduction maps
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 5.6
Status unassessed5.3 Subsampled randomized trigonometric transforms
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 6.1
Status unassessed6.1 Optimal bounds for Tensor Train decomposition
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 6.2
Status unassessed6.2 Eigenvalue systems arising from Hamiltonians
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 6.3
Status unassessed6.3 Matrix sign function
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 6.4
Status unassessed6.3 Matrix sign function
Numbered source pointer; current status and subsequent updates require checking in the linked source.
Problem 6.5
Status unassessedRemarks.
Numbered source pointer; current status and subsequent updates require checking in the linked source.