Informal seminar series on numerical analysis and applied mathematics aimed at students.
The aim of the meetings is to present numerical analysis research topics in an accessible manner and to involve interested students. The seminars will have an introductory first part and will also be accessible to those unfamiliar with the subject. They will be held mainly in Italian, in line with the informal tone of the series.
Master’s students and Bachelor’s students who are familiar with the contents of the Scientific Computing course are encouraged to attend.
Organised by PhD students from the University of Pisa and the Scuola Normale Superiore.
In this talk, we present a novel approach for value selection in fixed-pattern factorized sparse approximate inverse preconditioners. Unlike classical constructions that rely on algebraic Frobenius-residual criteria, the proposed strategy chooses admissible entries by directly optimizing spectral objectives of the congruent preconditioned operator. To make this practical for large-scale sparse matrices, we derive projected Krylov support-gradients implemented via a detached Rayleigh surrogate, which avoids differentiating through the Lanczos recurrence. Numerical experiments on finite-element test problems demonstrate that spectral value selection significantly improves fixed-support preconditioner performance, especially for symmetric indefinite saddle-point systems. Finally, we discuss an amortized node-edge model to predict factor entries across related matrices.
