Pavel Zhlobich

Matrix-free interior point method for compressed sensing problems

We consider a class of optimization problems for sparse signal reconstruction which arise in the field of compressed sensing (CS). A plethora of approaches and solvers exist for such problems, for example GPSR, FPC_AS, SPGL1, NestA,

Stability of QR-based fast system solvers for a subclass of quasiseparable rank one matrices

\mathbf{\ell _1\_\ell _s}

Green’s matrices

ℓ1_ℓs, PDCO to mention a few. CS applications lead to very well conditioned optimization problems and therefore can be solved easily by simple first-order methods. Interior point methods (IPMs) rely on the Newton method hence they use the second-order information. They have numerous advantageous features and one clear drawback: being the second-order approach they need to solve linear equations and this operation has (in the general dense case) an

A quasiseparable approach to five-diagonal CMV and Fiedler matrices

{\mathcal {O}}(n^3)

REPRINT OF: A quasiseparable approach to five-diagonal CMV and Fiedler matrices

O(n3) computational complexity. Attempts have been made to specialize IPMs to sparse reconstruction problems and they have led to interesting developments implemented in