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HomeMIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018Lecture 10: Survey of Difficulties with Ax = b
Lecture 10: Survey of Difficulties with Ax = b
49:36
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.
SummaryLarge 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
