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from Part I - Numerical Linear Algebra
Published online by Cambridge University Press: 29 September 2022
We study the solution of overdetermined systems of equations. Introduce weak, and in particular least squares solutions. For full rank systems, we show existence and uniqueness via the normal equations. We introduce projection matrices and the QR factorization. We discuss the computation of the QR factorization with the help of Householder reflectors. For rank defficient systems we prove the existence and uniqueness of a minimal norm least squares solution. We introduce the Moore-Penrose pseudoinverse, show how it relates to the SVD, and how it can be used to solve rank defficient systems.
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