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  or .)

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


§  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 4

§  Problem 5
Folkmar Bornemann: Solution of a problem posed by Jörg Waldvogel. Note of July 2003, Technische Universität München.

§  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 12
Geoff Vasil: Solution of Problem 12. Note of March 2019, University of Sydney.

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

§  Problem 14

§  Problem 15


§  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: 03/20/19 12:18 +0100 (FB)