M.A. Cherepniov, Version of block Lanczos-type algorithm for solving sparse linear systems, Bulletin mathématique de la Société des Sciences Mathématiques de Roumanie, Nouvelle Série, Vol. 53 (101), ...

Grade school math students are likely familiar with teachers admonishing them not to just guess the answer to a problem. But a new proof establishes that, in fact, the right kind of guessing is ...

Mathematics of Computation, Vol. 23, No. 108 (Oct., 1969), pp. 787-812 (26 pages) The mathematical and numerical least squares solution of a general linear system of equations is discussed.

The most famous quantum linear system solving algorithm is the Harrow-Hassidim-Lloyd (HHL) algorithm, which accelerates the solution of linear systems through quantum superposition and interference.

This algorithm is based on a combination of Variational Quantum Algorithms (VQA) and the classical shadow framework, overcoming the hardware resource bottlenecks of traditional quantum linear solver ...

The QLSP is a fundamental challenge in quantum computing, involving the use of quantum mechanics to solve linear equations. The new HQLS algorithm is said to reduce the need for large-scale controlled ...

One breakthrough came in 2010, when Dominic Berry, now at Macquarie University in Sydney, built the first algorithm for solving linear differential equations exponentially faster on quantum, rather ...