Algebraformer: A Neural Approach to Linear Systems
NeurIPS Workshop on Machine Learning and the Physical Sciences, 2025
Recent work in deep learning has opened new possibilities for solving classical algorithmic tasks using end-to-end learned models. In this work, we investigate the fundamental task of solving linear systems, particularly those that are ill-conditioned. Existing numerical methods for ill-conditioned systems often …
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.
A note on certain ergodicity coefficients
Special Matrices, vol. 3, pp. 175–185, 2015
We investigate two ergodicity coefficients $\phi_{|| \cdot ||}$ and $\tau_{n-1}$, originally introduced to bound the subdominant eigenvalues of nonnegative matrices. The former has been generalized to complex matrices in recent years and several properties for such generalized version have been shown so far. We provide …