The eigenproblem for an n-by-n matrix A is the problem of the approximation (within a relative error bound 2 ?b) of all the eigenvalues of the matrix A and computing the associated eigenspaces of allâ€¦ (More)

Elimination methods are highly effective for the solution of linear and nonlinear systems of equations, but reversal of the elimination principle can be beneficial as well: competent incorporation ofâ€¦ (More)

MBA algorithm inverts a structured matrix in nearly linear arithmetic time but requires a serious restriction on the input class. We remove this restriction by means of randomization and extend theâ€¦ (More)

For a Toeplitz or Toeplitz-like matrix T, we define a preconditioning applied to the symmetrized matrix TnT, which decreases the condition number compared to the one of TnT and even the one of T.â€¦ (More)

Highly effective polynomial root-finders have been recently designed based on eigen-solving for DPR1 (that is diagonal + rankone) matrices. We extend these algorithms to eigen-solving for the generalâ€¦ (More)

Matrix methods are increasingly popular for polynomial root-finding. The idea is to approximate the roots as the eigenvalues of the companion or generalized companion matrix associated with an inputâ€¦ (More)

We propose novel randomized preprocessing techniques for solving linear systems of equations and eigen-solving with extensions to the solution of polynomial and secular equations. According to ourâ€¦ (More)

Recent progress on root-finding for polynomial and secular equations largely relied on eigen-solving for the associated companion and diagonal plus rank-one generalized companion matrices. Byâ€¦ (More)