A study of error estimates for linear systems

This thesis examines methods to estimate errors of calculated solutions of linear systems. These methods include the traditional condition number, Skeel's condition numbers, and Chandrasekaran and Ipsen's component condition numbers. The thesis concentrates on condition numbers defined by Yang Cao and Linda Petzold. Their condition numbers can be used to estimate the error of the whole calculated solution or the error of just some components of the solution. Their condition numbers can also be estimated by using the adjoint equation and the random vectors as an application of the small sample statistical theory by Kenny and Laub. The numerical experiments are performed in Matlab using Cao and Petzold's method. Results from this method are compared with results produced by other methods to test the claim that this method can be implemented simply and is inexpensive to compute. Keywords: linear systems, error estimates, condition numbers, small sample statistical theory, selecting random point, uniform distribution, normal distribution.