Subject: Electronic Transactions on Numerical Analysis
ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS
Scope:
Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal
for the publication of significant new and important developments in numerical
analysis and scientific computing. Papers of the highest quality that deal with
the analysis of algorithms for the solution of continuous models and numerical
linear algebra are appropriate for ETNA, as are papers of similar quality that
discuss implementation and performance of such algorithms. New algorithms for
current or new computer architectures are appropriate provided that they are
numerically sound. However, the focus of the publication should be on the
algorithm rather than on the architecture. The journal is published by the Kent
State University Library in conjunction with the Institute of Computational
Mathematics at Kent State University. Mathematical Reviews will receive all
papers accepted for publication in the journal and review them as appropriate.
Dissemination:
On a monthly basis, accepted manuscripts will be posted in a directory which
is publicly accessible through Internet. The titles and abstract of these
manuscripts will be e-mailed to registered departments and individuals and
posted on public bulletin boards such as NA-digest. An individual who wishes
to obtain a copy of a current or back manuscript can get a copy through
anonymous FTP or by using a netlib-type mailer. We also plan to install
Gopher. All manuscripts will be available in Post Script format. The first
"issue" of ETNA will appear September 1, 1993. Funds made available by the
Kent State University Library and the Kent State University make free
subscription possible for at least three years. After this time period we
may have to charge an annual fee from institutional subscribers. Since the
operating costs for the journal are low, we envision that this fee will not
be above $100 for institutional subscribers. Everybody at the subscribing
institution will have access to ETNA by FTP, a netlib-type mailer or Gopher.
Submission, Acceptance and Refereeing:
Authors will normally submit papers for publication via e-mail, and they will
be required to submit their manuscript in LaTeX using macros we provide. All
papers will be refereed. Normally, an accepted manuscript will appear within
four weeks of the the author's last correction. There are no annual page
limitations, and therefore we are in a position to publish accepted
manuscripts faster than many other journal. Manuscripts can be submitted
NOW by sending them to the address etna@mcs.kent.edu.
Current Editorial Board:
L. Reichel Kent State University
editor-in-chief reichel@mcs.kent.edu
R.S. Varga Kent State University
editor-in-chief varga@mcs.kent.edu
A. Ruttan Kent State University
managing editor ruttan@mcs.kent.edu
G.S. Ammar Northern Illinois University
ammar@math.niu.edu
J. Demmel University of California, Berkeley
demmel@cs.berkeley.edu
J.J. Dongarra University of Tennessee
dongarra@cs.utk.edu
I.S. Duff Rutherford Appleton Laboratory
isd@directory.rl.ac.uk
M. Eiermann University of Karlsruhe
eiermann@ipmsun1.mathematik.uni-karlsruhe.de
A. George University of Waterloo
jageorge@provost.uwaterloo.ca
G.H. Golub Stanford University
golub@sccm.stanford.edu
W.B. Gragg Naval Postgraduate School
gragg@guinness.math.nps.navy.mil
M.H. Gutknecht Swiss Federal Institute of Technology
mhg@ips.ethz.ch
V. Mehrmann University of Bielefeld
mehrmann@math1.mathematik.uni-bielefeld.de
D.C. Sorensen Rice Univesity
sorensen@rice.edu
G.W. Stewart University of Maryland
stewart@brillig.umd.edu
O.B. Widlund New York University
widlund@widlund.cs.nyu.edu
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ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS
VOLUME 1, 1993
INDEX
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Pages 1-10.
Analysis of the linearly implicit mid--point rule for
differential--algebraic equations
by Claus Schneider
Abstract.
The error of the linearly implicit mid--point rule after $2m+1$ steps
is expanded in powers of $m^2$. We prove that the well-known expansion
for ordinary differential equations (an expansion in negative powers
of $m^2$) is perturbed by additional terms with non-negative powers of
$m^2$ for semi--explicit differential--algebraic equations of index one.
Hence, extrapolation in $m^{-2}$ will be of limited value only. The
complete expansion shows these limits and, furthermore, can be used to
derive an order 8 method of Rosenbrock type.
Key words.
Differential--algebraic equations, linearly implicit mid--point rule,
Rosenbrock--type methods, extrapolation.
AMS(MOS) subject classification.
65L05, 65B05, 58F99.
Files.
vol.1.1993/pp1-10.ps
Forward References.
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Pages 11-32.
BiCGstab($l$) for linear equations involving unsymmetric matrices with
complex spectrum
by Gerard L.G. Sleijpen and Diederik R. Fokkema
Abstract.
For a number of linear systems of equations arising from realistic
problems, using the Bi-CGSTAB algorithm of van der Vorst to solve these
equations is very attractive. Unfortunately, for a large class of equations,
where, for instance, Bi-CG performs well, the convergence of Bi-CGSTAB
stagnates. This was observed specifically in case of discretized advection
dominated PDE's. The stagnation is due to the fact that for this type of
equations the matrix has almost pure imaginary eigenvalues. With his
BiCGStab2 algorithm Gutknecht attempted to avoid this stagnation.ere, we
generalize the Bi-CGSTAB algorithm further, and overcome some shortcomings
of BiCGStab2. In some sense, the new algorithm combines GMRES($l$) and
Bi-CG and profits from both.
Key words.
Bi-conjugate gradients, non-symmetric linear systems, CGS, Bi-CGSTAB,
iterative solvers, GMRES, Krylov subspace.
AMS(MOS) subject classification.
65F10.
Files.
vol.1.1993/pp11-32.ps
Forward References.
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Pages 33-48.
A multishift algorithm for the numerical solution of algebraic Riccati
equations
by Gregory Ammar, Peter Benner, and Volker Mehrmann
Abstract.
We study an algorithm for the numerical solution of algebraic matrix
Riccati equations that arise in linear optimal control problems.
The algorithm can be considered to be a multishift technique, which uses
only orthogonal symplectic similarity transformations to compute
a Lagrangian invariant subspace of the associated Hamiltonian matrix.
We describe the details of this method and compare it with other
numerical methods for the solution of the algebraic Riccati equation.
Key words.
algebraic matrix Riccati equation, Hamiltonian matrix, Lagrangian
invariant subspace.
AMS(MOS) subject classification.
65F15, 15A24, 93B40.
Files.
vol.1.1993/pp33-48.ps
Forward References.
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Pages 49-71.
Zeros and local extreme points of Faber polynomials associated with
hypocycloidal domains
by Michael Eiermann and Richard S. Varga
Abstract.
Faber polynomials play an important role in different areas of constructive
complex analysis. Here, the zeros and local extreme points of Faber
polynomials for hypocycloidal domains are studied. For this task, we use
tools from linear algebra, namely, the Perron-Frobenius theory of
nonnegative matrices, the Gantmacher-Krein theory of oscillation matrices,
and the Schmidt-Spitzer theory for the asymptotic spectral behavior of
banded Toeplitz matrices.
Key words.
Faber polynomials, cyclic of index $p$ matrices, oscillation matrices.
AMS(MOS) subject classification.
30C15, 15A48, 15A57.
Files.
vol.1.1993/pp49-71.ps
Forward References.
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1. BECOMING A SUBSCRIBER TO ETNA.
To be included in ETNA's quarterly mailing list of the titles and abstracts
of papers published in ETNA, send an e-mail message to etna@mcs.kent.edu
with the subject "ETNA Registration".
2. ACCESSING ETNA USING GOPHER.
ETNA is running a gopher server. Its hostname is etna.mcs.kent.edu.
If you are running gopher on your system the command
gopher etna.mcs.kent.edu
will connect you directly to ETNA. Provided your system is suitably
configured, keyword searches and the on-line-graphical display of
papers will then be available. The ETNA directory, "viewers", contains
the source files for programs that will provide most UNIX workstations
with direct-display and keyword-search capabilities. Contact your system
admistrator about installing these programs.
3. OBTAINING AN ETNA PAPER WITH FTP.
Papers can be obtained at any time from ETNA via anonymous ftp from
etna.mcs.kent.edu. A paper's location will always correspond to
its reference. For instance, a paper which is referenced as
"...,Elec. Trans. Numer. Anal., Vol 1, 1993, pp. 11-35", will be stored
in the directory "vol.1.1993", and its file name will be "pp11-35.ps".
To obtain that paper using ftp
a) ftp etna.mcs.kent.edu
b) login as anonymous
c) enter your e-mail address as your password
d) cd to vol.1.1993
e) get pp11-35.ps
To obtain only the list of titles and abstract for the papers published
is volume 1 of ETNA, proceed repeat a)-d) above but change e) to
e) get index
4. OBTAINING AN ETNA PAPER VIA E-MAIL.
ETNA is using a mailer program which will scan incoming e-mail messages
for requests and then e-mail the requested file to the sender. The program
was written by Eric Grosse for netlib and modified slightly by Arden
Ruttan for ETNA.
A PostScript file of any paper published in ETNA may be obtained by sending
an e-mail message to "mailer@etna.mcs.kent.edu" containing a phrase of the
form "send pagenumber from vol.number.year". For instance, to use
ETNA's mailer to obtain a paper which is referenced as
"...,Elec. Trans. Numer. Anal., Vol 1, 1993, pp. 11-35",
send e-mail to "mailer@etna.mcs.kent.edu" containing the phrase
"send pp11-35.ps from vol.1.1993".
To obtain only the list of titles and abstract for the papers published
in volume 1 of ETNA, send an e-mail message to "mailer@etna.mcs.kent.edu"
containing the phrase "send index from vol.1.1993".
The requested paper will be e-mailed to you in several pieces. The subject
of each piece of e-mail indicates the number of that piece. To
reconstruct the original file,
a) Edit each piece deleting all lines that are not strictly between
the two occurrence of the phrase "CUT HERE............"
including the lines containing those phrases.
b) Using the file containing piece 1, successively append
the remaining pieces in order to the END of the that file.
Unix users may also use the following script which will automatically
reconstruct the orginal PostScript file.
#!/bin/sh
# This is a shell script which will re-assemble the PostScript file
# mailed to you by ETNA's mailer program. To use this script
# 1) Copy this script to a file in an empty directory and name it reassm.
# 2) Save each mail message from ETNA with a unique name in the
# directory which contains this file.
# 3) Change to that directory and execute the command
# sh reassm
# or alternately you can
# 1) Change to a directory containing this a script in a file.
# 2) Save each mail message from ETNA with a unique name but with a common
# prefix shared by only the ETNA files. For example, you could save the
# respective ETNA files in ff1, ff2, ...
# 3) Assuming the name of this file is reassm, execute the command
# sh reassm ff
ls $1* | grep -v $0 > .f$$
for file in `cat .f$$`
do
echo $file
awk 'BEGIN{i=0};$1=="#!/bin/sh" {i=1};{if (i>0) print $0}' $file > .awk$$
/bin/sh .awk$$
done
rm .f$$
rm .awk$$
5. SUBMITTING A PAPER TO ETNA.
To obtain information as to how to submit a paper to ETNA, ftp the file
"info-for-authors" which is located in the directory "etna-info".
Alternately you may send an e-mail message to "mailer@etna.mcs.kent.edu"
containing the phrase "send info-for-authors from etna-info".