In this book I have attempted to trace the development of numerical
analysis during the period in which the foundations of the modern theory
were being laid. To do this I have had to exercise a certain amount of
selectivity in choosing and in rejecting both authors and papers. I have
rather arbitrarily chosen, in the main, the most famous mathematicians
of the period in question and have concentrated on their major works in
numerical analysis at the expense, perhaps, of other lesser known but
capable analysts. This selectivity results from the need to choose from
a large body of literature, and from my feeling that almost by
definition the great masters of mathematics were the ones responsible
for the most significant accomplishments. In any event I must accept
full responsibility for the choices. I would particularly like to
acknowledge my thanks to Professor Otto Neugebauer for his help and
inspiration in the preparation of this book. This consisted of many
friendly discussions that I will always value. I should also like to
express my deep appreciation to the International Business Machines
Corporation of which I have the honor of being a Fellow and in
particular to Dr. Ralph E. Gomory, its Vice-President for Research, for
permitting me to undertake the writing of this book and for helping make
it possible by his continuing encouragement and support.