clopen.solutions

Open problems

980 registered problems.

OP-00115 Lean verified
Polynomial trace-error factor after exactly the target rank of pivots
NA · low-rank approximations · OpenProblemsInNLA · pivoted Cholesky factorizations
OP-00116 Lean verified
Improve the randomized LU squared-error factor to 2^k
NA · low-rank approximations · OpenProblemsInNLA · pivoted LU factorizations
OP-00118 Lean verified
Critical-point counts for symmetric rank-two approximation with diagonal zeros
AG · Euclidean distance degrees · low-rank approximations · OpenProblemsInNLA · symmetric matrices
OP-00169 Partially resolved
Optimal pivot count for RPCholesky trace approximation
NA · low-rank approximations · Nyström approximations · OpenProblemsInNLA · pivoted Cholesky factorizations
OP-00171 Partially resolved
Optimal query complexity of spectral rank-k approximation
NA · Krylov subspace methods · low-rank approximations · OpenProblemsInNLA · query complexity
OP-00172 Open
Query complexity from Schatten to spectral norms
NA · low-rank approximations · OpenProblemsInNLA · query complexity · Schatten norms
OP-00207 Solution claimed
Improve the worst-case approximation factor for prescribed tensor-train ranks
NA · approximation algorithms · low-rank approximations · OpenProblemsInNLA · tensor-train decompositions
OP-00237 Solution claimed
Clustered singular-value gaps in randomized block Krylov approximation
NA · Krylov subspace methods · low-rank approximations · OpenProblemsInNLA · singular value gaps
OP-00238 Solution claimed
Sharp joint rank and accuracy dependence for strong ℓₚ subspace coresets
NA · coresets · low-rank approximations · OpenProblemsInNLA · subspace approximation
OP-00240 Solution claimed
Concave-function transfer of spectral low-rank error
NA · low-rank approximations · matrix functions · Nyström approximations · OpenProblemsInNLA
OP-00241 Solution claimed
Concave-function transfer of Frobenius low-rank error
NA · low-rank approximations · matrix functions · Nyström approximations · OpenProblemsInNLA
OP-00242 Solution claimed
Constant-loss nuclear-error transfer without matrix ordering
NA · low-rank approximations · matrix functions · OpenProblemsInNLA · operator monotone functions
OP-00245 Solution claimed
Critical-point count for corank-one approximation with a fixed zero
AG · determinantal varieties · Euclidean distance degrees · low-rank approximations · OpenProblemsInNLA
OP-00260 Solution claimed
Complexity of globally optimal nonnegative rank-two approximation
NA · low-rank approximations · nonnegative matrix factorizations · OpenProblemsInNLA