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.
To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.