Published online by Cambridge University Press: 05 August 2012
The need to solve large linear systems of algebraic equations arises in almost any mathematical model, as illustrated in the instances below. In particular, we go into some detail regarding electrical networks. The most common method used to solve such linear systems is based on factorization of the matrix in triangular factors, which is discussed and shown to be equivalent to the Gaussian elimination method (learned in almost any elementary course in algebra).
We present this method in a form that can be the basis for a computer algorithm. When one wants to solve very large systems of equations, it is important to know how computational complexity grows with the size of the problem. This topic is also addressed, including the case where the matrix has a special structure in the form of a bandmatrix. The solution of tridiagonal systems is considered in particular detail. In addition, some basic dimension theory for matrices, such as the relation between rank and the dimension of the nullspace, is discussed and derived using the factored form of the matrix.
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.