Ebook: A collection of matrices for testing computational algorithms

This monograph is intended primarily as a reference book for numerical analysts and others who are interested in computational methods for solving problems in matrix algebra. It is well known that a good mathematical algorithm may or may not be a good computational algorithm. Consequently, what is needed is a collection of numerical examples with which to test each algorithm as soon as it is proposed. It is our hope that the matrices we have collected will help fulfill this need.
The test matrices in this collection were obtained for the most part by searching the current literature. However, four individuals who had begun collections of their own contributed greatly to this effort by providing a large number of test matrices at one time.
First, Joseph Elliott's Master's thesis [18] provided a large collection of tridiagonal matrices. Second, Mrs. Susan Voigt, of the Naval Ship Research and Development Center, contributed a varied collection of matrices. Third, Professor Robert E. Greenwood, of The University of Texas at Austin, provided a valuable list of references along with his collection of matrices and determinants. Finally, just as this work was nearing completion, the collection of Dr. Joan Westlake [60] was discovered. Her collection of 41 test matrices contained seven which we had overlooked; therefore, they were added.