clopen.solutions

Open problems

980 registered problems.

OP-00170 Partially resolved
Optimal trace-estimation complexity using Kronecker matrix-vector queries
NA · Kronecker products · OpenProblemsInNLA · query complexity · trace estimation
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-00178 Partially resolved
Optimal matvec query complexity of HODLR approximation
NA · HODLR matrices · matrix-vector queries · OpenProblemsInNLA · query complexity
OP-00228 Solution claimed
Find a near-largest nonnormal eigenvalue using few matrix-vector products
NA · eigenvalue algorithms · nonnormal matrices · OpenProblemsInNLA · query complexity
OP-00246 Solution claimed
Pure relative error for approximation by a linear matrix family
NA · matrix-vector queries · OpenProblemsInNLA · query complexity · structured matrices
OP-00247 Solution claimed
Nonadaptive queries for finite-family matrix approximation
NA · matrix-vector queries · nonadaptive algorithms · OpenProblemsInNLA · query complexity
OP-00324 Open
Aaronson–Ambainis influential-variable conjecture
CO · AIM Open Applied Problems · Boolean functions · influences · quantum query complexity