3 problems

Let $m$ be the sampling number, let $\lambda=\lVert A\rVert_2$ and $\phi=\lVert A\rVert_F$ for a symmetric matrix $A$, and let $\varepsilon_{\mathrm{abs}}$ be the threshold appeari…

Let $m$ be the sampling number, let $mu=r_{\mathrm{eff}}(A)$ for a nonzero symmetric positive semidefinite matrix $A$, and let $\varepsilon_{\mathrm{rel}}$ be the threshold appeari…

Let $\boldsymbol{A}$ be a matrix, let $\boldsymbol{A}_k$ be its best rank-$k$ approximation, and let $\boldsymbol{U}_k$ contain the top-$k$ left singular vectors of…