4 problems

Let $A$ be a matrix, let $u$ and $v$ be vectors, and consider the rank-one perturbed linear system $(A+uv^T)x=b$. A system is numerically nonsingular when it is sufficiently nonsin…

Let $A$ be a matrix, let $u$ and $v$ be vectors, and let $\tilde A=A+uv^T$. Let $\epsilon_M$ denote the unit roundoff, and let $\kappa(\cdot)$ denote the matrix condition number. S…

Let $A$ be a matrix, let $u$ and $v$ be vectors, and let $\tilde A=A+uv^T$. Let $\epsilon_M$ denote the unit roundoff, and let $\kappa_2(\cdot)$ denote the matrix 2-norm condition…

Right-preconditioned GMRES bounds conjecture. Under this condition, right-preconditioned GMRES is backward stable, and similar bounds can be proved for the quantities in Table. The…