Matrix Computations and Semiseparable Matrices: Vol. 1, Linear Systems; Vol. 2, Eigenvalue and Singular Value Methods
Jonathan Gillard · Journal of the Royal Statistical Society Series A (Statistics in Society) · 2011
Both of these volumes are concerned with semiseparable matrices. Avoiding technicalities, matrices with this structure have properties which permit the development of fast and precise algorithms for common procedures such as Gaussian elimination (among others). Both the theoretical underpinnings and the practical implementation of the results that are contained in the books are detailed. MATLAB code to implement many of the routines is included on an accompanying Web site. Throughout the volumes key references are highlighted, and some commentary on the application of the results described is given. This is particularly useful to get a feel of how the results may be applied within a statistical setting. These texts, strictly speaking, are not statistical texts. They are very much focused on the description of analytic results with some toy examples. It may be that some statisticians would find topics in this book of interest especially if they are involved in the programming of high level matrix algebra routines. However, there are few explicit statistical examples. Some comment on covariance matrices as semiseparable matrices is given, but that is nearly all. This is not a flaw of these books; they are not specifically written with a statistical audience in mind. People with an interest in matrix algebra are likely to find the volumes interesting, and academics may be able to apply the results within their statistical research.