NA Digest Sunday, August 7, 1994 Volume 94 : Issue 32

Today's Editor:

Cleve Moler

The MathWorks, Inc.

moler@mathworks.com

Today's Topics:
• Typo in "Templates..."
• Corrected Painless Conjugate Gradient Report
• Representation Errors for Bandlimited Functions
• Solution to a Block Toeplitz System
• Numerical Methods: Matlab Programs
• Change of Address for Keh-Ming Shyue
• Mathematical Support for Molecular Biology
• Conference on Modelling and Optimization
• A Workshop on Sparse Matrices
• Rocky Mountain Numerical Analysis Conference
• Object-Oriented Numerics Conference
• Positions at Univ. of Ioannina
• Position at University of Newcastle
• Positions at Dublin City University
• Position in Ticino, Switzerland
• Position at U. Texas, Permian Basin
• Position at the University of Liverpool
• Contents, Constructive Approximation
• Contents, Surveys on Mathematics for Industry
• Contents, SIAM Math Analysis
• Contents, SIAM Discrete Mathematics

Submissions for NA Digest:

Information about NA-NET:

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From: Dirk laurie <WSKDPL@puknet.puk.ac.za>
Date: Thu, 04 Aug 94 20:00
Subject: Typo in "Templates..."

There is a typographical error in the QMR algorithm on page 24 of
"Templates for the Solution of Linear Systems: Building Blocks for
Iterative Methods" by Richard Barrett et al (SIAM 1994). The matrix M_2
on Line 4 of the pseudocode should be replaced by its transpose.
Correction of this error dramatically improves convergence in the case
where M_2 is upper triangular.

Dirk Laurie


------------------------------

From: Jonathan Shewchuk <Jonathan.R.Shewchuk@DUCK.WARP.CS.CMU.EDU>
Date: Fri, 5 Aug 94 00:35:07 EDT
Subject: Corrected Painless Conjugate Gradient Report

The corrected version of my Conjugate Gradient report is now available by
anonymous FTP:

An Introduction to the Conjugate Gradient Method
Without the Agonizing Pain
(Edition 1 1/4, Corrected)

Jonathan Richard Shewchuk
jrs@cs.cmu.edu

If you obtained a copy of the original report, please burn it and replace it
with the new one. The new version corrects all errors that I know of, and adds
a few more pages of intuition. Note that the new version is *NOT* available
from the same FTP site as the original version. (The copy at that site is
still the old version with the nasty errors.)

The corrected report is available by anonymous FTP to WARP.CS.CMU.EDU (IP
address 128.2.209.103) in the directory quake-papers/ . You may choose from
the files:

painless-conjugate-gradient.ps (Report; 600 and 300 dpi PostScript)
- or -
painless-conjugate-gradient.ps.gz (Gnuzip-compressed report)
- or -
painless-conjugate-gradient1.ps.gz \ (Compressed report broken up into
painless-conjugate-gradient2.ps.gz \ four PostScript files for small-
painless-conjugate-gradient3.ps.gz / memory printers. 300 dpi; looks
painless-conjugate-gradient4.ps.gz / ugly on 600 dpi printers.)

Also in the quake-papers/ directory:

painless-conjugate-gradient.abs (Abstract)
painless-conjugate-gradient-figs.ps (Full-page classroom transparencies)
painless-conjugate-gradient-figs.ps.gz (Gnuzip-compressed transparencies)

Remember to set FTP to binary mode when obtaining compressed files. The report
itself is formatted for a two-sided printer.

Comments and corrections are welcome and encouraged. Many thanks to all of
you who sent me comments about the original version; I can't begin to say how
helpful NA Digest readers have been. For those of you who have been waiting
too long for the corrected version, thanks for your patience.

Jonathan


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From: Raghu Machiraju <raghu@cis.ohio-state.edu>
Date: Thu, 4 Aug 1994 09:18:58 -0400 (EDT)
Subject: Representation Errors for Bandlimited Functions

Any band-limited signal (1-D to begin with) can be resampled or interpolated
using the Cardinal functions S(k,h), namely:

        f(x) = Sum S(k,h)(x) f(kh)

                k

        f(x) = Sum S(k,h)(x) f(kh) + Sum S(k,h)(x) f(kh)

                -n<=k <=n            abs(k) > n

        f(x) = g(x,n,h) + e(x,n,h)

      --            --   --    --   --    --

      |  a  b  c  b  |   |  x1  |   |  y1  |

      |  b  a  b  c  | * |  x2  | = |  y2  |

      |  c  b  a  b  |   |  x3  |   |  y3  |

      |  b  c  b  a  |   |  x4  |   |  y4  |

      --            --   --    --   --    --