Appendix D

More Problems

*Whatever the details of the matter, it finds
me too absorbed by numerous
occupations for me to be able to devote my attention to it immediately.*

―John Wallis, upon hearing about a problem posed by Fermat in 1657

To help
readers experience first-hand the excitement, frustration, and joy of working
on a challenging numerical problem, we have included in the book a selection of 22 problems in the same style as
Trefethen's 10.

If you solve
one of these and wish to share your solution, we will be happy to receive it.
(Send e-mail to bornemann@tum.de or wagon@macalester.edu .)

*Please
note that Problem 15 has not been transcribed correctly in the first printing.** *(Correct version and
further information here.)

Solutions

§
Problem 1

Thomas Schmelzer, Robert Baillie: *Summing a curious, slowly
convergent series*. Amer. Math. Monthly 115, pp. 525-540 (2008).

§
Problem 2

David Smith: *On a slowly converging sum*. Note of November 2003,
Loyola Marymount University.

§
Problem 3

Daniel Lichtblau: *The evaluation of Knopfmacher's
curious limit*. Note of August 2000, Wolfram Research.

§
Problem 5__
__Folkmar Bornemann:

§
Problem 7

Thomas Dickens: *SIAM 100-Digit Challenge Extra
Problem Number 7*. Note of October 2007, ExxonMobil Upstream Research
Company.

§
Problem 8

Joris Van Deun, Ronald Cools:
*Algorithm
858: Computing infinite range integrals of an arbitrary product of Bessel
functions**.* ACM Trans. Math. Softw. 32, pp. 580-596 (2006).

§
Problem 9

David Smith: *Solution of Problem 9*. Note of February 2014, Loyola
Marymount University.

§
Problem 11

David Smith: *Solution of Problem 11*. Note of January 2006, Loyola
Marymount University.

§
Problem 13

David Smith: *Solution of Problem 13*. Note of February 2014,
Loyola Marymount University.

Links

§
A selection of five
problems has been published in SIAM's electronic *Problems and Solutions*,
edited by Cecil C. Rousseau

§
The
SIAM student chapter of Rice University has set up five new problems as a *50-Digit
Challenge. *The winner, Thomas Schmelzer from Oxford University, has posted
his solution to the web.

This is a web
page for the book:

Folkmar Bornemann, Dirk
Laurie, Stan Wagon, Jörg Waldvogel: *The SIAM 100-Digit Challenge, A Study in
High-Accuracy Numerical Computing*. Society of Industrial and Applied
Mathematics (SIAM), Philadelphia, 2004.

last modified: 02/07/14
11:54 +0100 (FB)