SIAM Homepage | Search Catalog | New Books | Author Index | Series Index | Title Index | View My Shopping Cart

The catalog and shopping cart are hosted for SIAM by EasyCart. Your transaction is secure. If you have any questions about your order, contact

Purchase Now!

Scientific Computation on Mathematical Problems and ConjecturesScientific Computation on Mathematical Problems and Conjectures

Richard S. Varga

CBMS-NSF Regional Conference Series in Applied Mathematics 60

"Let me state at the outset that this monograph is a gem. It contains six completely independent chapters devoted to six different areas. The unifying theme is that all of the problems are drawn from classical analysis with a strong tilt toward approximation theory. The unique part of the monograph is how high-precision numerical calculations can play a creative role in this area. In fact, it is possibly fair to say that the monograph is a sequence of challenging and interesting problems, where both hard analysis and sophisticated computing techniques are brought to bear to develop rigorous proof of interesting conjectures, or in some cases, used to establish counterexamples." - George J. Fix, SIAM Review, June 1993.

"This book contains fascinating accounts of how some longstanding mathematical problems could be solved after an accumulation of efforts by many mathematicians and the use of highly accurate floating- point computations. At the same time it shows that there are still a lot of unsolved mathematical problems, the solution of which may require deep mathematics, but probably also fast computers and highly-accurate numerical software." -- Herman J.J. te Riele, Mathematical Reviews, Issue 92b.

Studies the use of scientific computation as a tool in attacking a number of mathematical problems and conjectures. In this case, scientific computation refers primarily to computations that are carried out with a large number of significant digits, for calculations associated with a variety of numerical techniques such as the (second) Remez algorithm in polynomial and rational approximation theory, Richardson extrapolation of sequences of numbers, the accurate finding of zeros of polynomials of large degree, and the numerical approximation of integrals by quadrature techniques.

The goal of this book is not to delve into the specialized field dealing with the creation of robust and reliable software needed to implement these high-precision calculations, but rather to emphasize the enormous power that existing software brings to the mathematician's arsenal of weapons for attacking mathematical problems and conjectures.

Scientific Computation on Mathematical Problems and Conjectures includes studies of the Bernstein Conjecture of 1913 in polynomial approximation theory, the "1/9" Conjecture of 1977 in rational approximation theory, the famous Riemann Hypothesis of 1859, and the Polya Conjecture of 1927. The emphasis of this monograph rests strongly on the interplay between hard analysis and high-precision calculations.


Chapter 1: The Bernstein Conjecture in Approximation Theory; Chapter 2: The "1/9" Conjecture and Its Recent Solution; Chapter 3: Theoretical and Computational Aspects of the Riemann Hypothesis; Chapter 4: Asymptotics for the Zeros of the Partial Sums of exp(z); Chapter 5: Real vs. Complex Best Rational Approximation; Chapter 6: Generalizations of Jensen's Inequality for Polynomials Having Concentration at Low Degrees.

1990 / vi + 122 pages / Softcover / ISBN-13: 978-0-898712-57-5 / ISBN-10: 0-89871-257-2 /
List Price $53.50 / SIAM/CBMS Member Price $37.45 / Order Code CB60
Quantity desired

Search our catalog for:

Shopping cart provided by:
Select quantity and list or member price and then click the "Click to Order" button to add books to your shopping cart.
Banner art adapted from a figure by Hinke M. Osinga and Bernd Krauskopf (University of Auckland, NZ.)