2026
Neural-HSS: Hierarchical Semi-Separable Neural PDE Solver
International Conference on Machine Learning (ICML), 2026
Deep learning-based methods have shown remarkable effectiveness in solving PDEs, largely due to their ability to enable fast simulations once trained. However, despite the availability of high-performance computing infrastructure, many critical applications remain constrained by the substantial computational costs …
2016
Lower triangular Toeplitz-Ramanujan systems whose solution yields the Bernoulli numbers
Linear Algebra and its Applications, vol. 496, pp. 510–526, 2016
We prove that the Bernoulli numbers satisfy some special lower triangular Toeplitz systems of linear equations. One of these systems has a strong link with eleven Ramanujan’s linear equations satisfied by the first eleven Bernoulli numbers.
2013
Optimal Rank Matrix Algebras Preconditioners
Linear Algebra and its Applications, vol. 438, pp. 405–427, 2013
When a linear system $Ax = y$ is solved by means of iterative methods (mainly CG and GMRES) and the convergence rate is slow, one may consider a preconditioner $P$. The use of such preconditioner changes the spectrum of the matrix defining the system and could result into a great acceleration of the convergence rate. …