At a meeting in Moscow in June 2005, Gil Strang suggested that there be a collection of Gene Golub's work to highlight his many important contributions to numerical analysis. The three of us were honored to undertake this pleasant task, with publication timed for February "29", 2007, the 75th anniversary of Gene's birth.
Gene chose 21 papers to include here, and we are grateful to the publishers for permission to reprint these works. We asked each of the coauthors to write about how the paper came to be written. These short essays reveal a lot about Gene's working style - his quickness and creativity, his ability to draw together threads from diverse areas, and the beauty of his ideas. They also illustrate the serendipity of mathematical discovery and demonstrate that mathematics research can be done anywhere from an office to an amusement park.
Gene's work is broad as well as deep, and we have divided the papers into five groups: iterative methods for linear systems, solution of least squares problems, matrix factorizations and applications, orthogonal polynomials and quadrature, and eigenvalue problems. To put the work in context, we asked a leading expert to write a commentary on each group of papers, putting them into historical perspective. It is a testimony to the high regard in which Gene is held by his colleagues, that the first five people we contacted agreed to write these commentaries. We are very grateful to Anne Greenbaum, Ake Bjorck, Nicholas Higham, Walter Gautschi, and G. W. (Pete) Stewart; their careful work will be a great aid to numerical researchers now and in the future.
We are also pleased to be able to include a biography of Gene, drawn from conversations with him, as well as photos collected from Gene and his friends.
And so we present this volume as a gift to Gene, gathering some of his many important gifts to the community. We treasure his friendship, look forward to his 19th birthday in 2008, and wish him many more happy and productive years.