From: Jeffery J. Leader Subject: Re: Book on Numerical Integration Date: Sun, 10 Sep 2000 15:50:06 -0500 Newsgroups: sci.math.num-analysis Summary: [missing] On Sun, 10 Sep 2000 22:49:45 +0300, "N&J" wrote: >Davis and Rabinowitz, Methods of Numerical Integration A classic! I'm glad I have a copy. It set the standard, in my (biased) opinion, until the relatively recent "Computational Integration" by Krommer and Ueberhuber (SIAM, 1998) which I recommend. It addresses most, at least, of what you mentioned in your message. It does not however contain software, though it discusses specific IMSL/NAG/etc. routines in some detail. See: http://www.siam.org/catalog/mcc07/ot53.htm ============================================================================== From: trhoffend@mmm.com (Tom Hoffend) Subject: Re: Book on Numerical Integration Date: 18 Sep 2000 13:21:47 GMT Newsgroups: sci.math.num-analysis Jeffery J. Leader wrote: > On 14 Sep 2000 13:39:26 GMT, trhoffend@mmm.com (Tom Hoffend) wrote: >>I have been trying to recall from memory a transformation (from >>Davis and Rabinowitz) of Gauss-Legendre weights/nodes for integrals >>of functions f(x) against kernels of the type a/sqrt(a^2+x^2), >>designed in particular for the case where $0>code in my own collection of "golden oldies" type of tools that I wrote >>about 10 years ago that has the transformation included in it, but I can't >>remember the logic. It had something to do with a complex map of ellipses. > Could you be thinking about the material on pg. 177 of the 2nd ed., > covering "Singularities off but near the Interval of Integration," > which starts as follows: > "For singularities on or near the imaginary axis, the following > procedure, based on the conformal mapping of the connected ovals of > Cassini onto the circle, has been suggested by Rabinowitz and > Richter." > If so, the reference is to Rabinowitz and Richter, "to be published" > (!), and the example given is for the kernel 1/(a^2+x^2)^2. It's only > two pages; I can send you a photocopy if you wish. The basic idea is > intended for Cauchy principal value integrals and is related to > Lether's method of subtracting out the singularities; Krommerer and > Ueberhuber cover the subject (singular/nearly singular problems) very > well and do address these ideas.. Thats it! Now I remember searching the literature to see if that work was ever published as a journal article, and I am sure that it was not. No need to send a photocopy - I am having our library borrow the book on interlibrary loan (thank you for offering!). This was more of a curiousity for me at this time rather than an immediate need for an algorithm. I am definitely ordering the book by Krommerer and Ueberhuber, too. TRH -- Thomas R. Hoffend Jr., Ph.D. EMAIL: trhoffend@mmm.com 3M Company 3M Center Bldg. 201-1C-18 My opinions are my own and not St. Paul, MN 55144-1000 those of 3M Company. Opinions expressed herein are my own and may not represent those of my employer.