Scientific Computations on Mathematical Problems and Conjectures (CBMS-NSF Regional Conference Series in Applied Mathematics) [Paperback]

Richard S. Varga (Author)

Book Description

Publication Date: January 1, 1987 | ISBN-10: 0898712572 | ISBN-13: 978-0898712575

This book 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.

Editorial Reviews

Review

"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.

About the Author

Richard S. Varga is University Professor of Mathematics and Director of the Institute for Computational Mathematics at Kent State University. He is the author of five books and over 150 publications in numerical analysis, approximation theory, linear algebra, and complex analysis. He serves on the editorial boards of several scientific journals, including the SIAM Journal on Matrix Analysis and Applications. Dr. Varga has been a consultant to Gulf Research Laboratories, Bettis Atomic Power Laboratory, Argonne National Laboratory, Los Alamos Scientific Laboratory, Lawrence Livermore Laboratory, Bell Laboratories, and NASA Lewis Research Center. He is a member of SIAM, AMS, and Sigma XI.

Product Details

• Paperback: 128 pages
• Publisher: Society for Industrial Mathematics (January 1, 1987)
• Language: English
• ISBN-10: 0898712572
• ISBN-13: 978-0898712575
• Product Dimensions: 9.6 x 6.6 x 0.3 inches
• Shipping Weight: 7.2 ounces (View shipping rates and policies)
• Amazon Best Sellers Rank: #4,057,444 in Books (See Top 100 in Books)

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