Lecture 10: Survey of Difficulties with Ax = b

Om kurset

Description The subject of this lecture is the matrix equation \(Ax = b\). Solving for \(x\) presents a number of challenges that must be addressed when doing computations with large matrices. Summary Large condition number \(\Vert A \Vert \ \Vert A^{-1} \Vert\) \(A\) is ill-conditioned and small errors are amplified. Undetermined case \(m < n\) : typical of deep learning Penalty method regularizes a singular problem. Related chapter in textbook: Introduction to Chapter II Instructor: Prof. Gilbert Strang