3 problems

The dense Hermitian diagonalization problem asks for the eigenvalues and eigenvectors of an $n\times n$ Hermitian matrix using exact arithmetic; let $\omega$ denote the exponent of…

Let $n$ be the matrix dimension and let $varepsilon>0$ denote the target accuracy for the Hermitian eigenvalue algorithm. Logarithmic-precision conjecture. $O(\log(n/\varepsilon))$…

Let a matrix be reduced to Hessenberg form, and let the resulting errors be compared with the condition numbers governing the sensitivity of its characteristic-polynomial coefficie…