Chapter 16

This chapter presents linear least-squares. The normal equations are motivated by a figure showing that b − Ax should be normal to Ax. It is then shown that if m ≥ n, there is a unique least-squares solution if and only if x satisfies the normal equations. Also, x is unique if and only if A has full rank. The pseudoinverse or the Moore-Penrose generalized inverse is presented, and the condition number of an m × n matrix m ≥ n is defined using the pseudoinverse. There are three basic techniques for solving the overdetermined least-squares problem, m ≥ n, solving the normal equations, using the reduced QR decomposition, and using the reduced SVD. The most commonly used is the QR decomposition. The ...

Start Free Trial

No credit card required