This is the repository of course materials for the 18.335J/6.7310J course at MIT, taught by Dr. Shi Chen, in Spring 2025. Topics: Advanced introduction to numerical linear algebra and related ...

For a square matrix ( A ), an eigenvalue ( \lambda ) and a corresponding eigenvector ( v ) are defined by the equation: [ Av = \lambda v ] The eigenvalue ( \lambda ) is a scalar that scales the ...

Algebraic multigrid (AMG) methods have emerged as a crucial tool for efficiently solving large, sparse linear systems, particularly those arising in complex scientific and engineering simulations.

Presenting an algorithm that solves linear systems with sparse coefficient matrices asymptotically faster than matrix multiplication for any ω > 2. Our algorithm can be viewed as an efficient, ...

Analysis and application of numerical methods for solving large systems of linear equations, which often represent the bottleneck when computing solutions to equations arising in fluid mechanics, ...

This course provides an introduction to mathematical logic, linear algebra and numerical analysis. Linear algebra aims to solve large systems of equations and to analyse these solutions, while ...

Book Abstract: Linear complementarity problems (LCPs) have for many years been used in physics-based animation to model contact forces between rigid bodies in contact. More recently, LCPs have found ...