Cambridge Univ. Press, Cambridge 2001

ISBN-0-521-333237 (hardback), ISBN 0-521-336104 (paperback)

Table of Contents

Cover

A. Neumaier

**
Interval Methods for Systems of Equations
**

Encyclopedia of Mathematics and its Applications 37,

Cambridge Univ. Press, Cambridge 1990

(out of print)

Slides on robotics applications

A. Neumaier, Certified error bounds for uncertain elliptic equations

A. Neumaier, Computer-assisted proofs

H. Schichl and A. Neumaier, Interval Analysis on Directed Acyclic Graphs for Global Optimization

H. Schichl and A. Neumaier, Exclusion regions for systems of equations

A. Neumaier, A Gerschgorin-type theorem for zeros of polynomials

A. Neumaier, Taylor forms - use and limits, Reliable Computing 9 (2002), 43-79.

A. Neumaier, Grand challenges and scientific standards in interval analysis, Reliable Computing 8 (2002), 313-320.

A. Neumaier, Generalized Lyapunov-Schmidt reduction for parametrized equations at near singular points, Linear Algebra Appl. 324 (2001), 119-131.

R.B. Kearfott, J. Dian and A. Neumaier, Existence verification for singular zeros of nonlinear systems, SIAM J. Numer. Anal. 38 (2000), 360-379.

A. Neumaier, On Shary's algebraic approach for linear interval equations, SIAM J. Matrix Anal. Appl. 21 (2000), 1156-1162.

A. Neumaier, A simple derivation of the Hansen-Bliek-Rohn-Ning-Kearfott enclosure for linear interval equations, Reliable Computing 5 (1999), 131-136.

T. Rage, A. Neumaier and C. Schlier, Rigorous verification of chaos in a molecular model, Phys. Rev. E. 50 (1994), 2682-2688.

A. Neumaier, Global, rigorous and realistic bounds for the solution of dissipative differential equations. Part I: Theory, Computing 52 (1994), 315-336.

A. Neumaier, The wrapping effect, ellipsoid arithmetic, stability and confidence regions, Computing Supplementum 9 (1993), 175-190.

A. Neumaier,
The enclosure of solutions of parameter-dependent systems of
equations.
In: Reliability in Computing (ed. by R.E. Moore).
Acad. Press, San Diego 1988, pp. 269-286.

scanned text

Auto-validating numerical methods (A course by Warwick Tucker)

Interval analysis in MATLAB (Hargreaves)

Interval Arithmetic (Van Emden)

Interval Computations: Introduction, Uses, and Resources (Kearfott)

Some Applications of Interval Computations (Vladik Kreinovich)

Vorlesung globale Optimierung (Dietmar Ratz, in German)

Self-Validated Numerical Methods and Applications (ps.gz, 538K; de Figueiredo and Stolfi)

Interval methods for bounding the range of polynomials and solving systems of nonlinear equations (ps, Ph.D. thesis by Volker Stahl)

Fields Institute Informal Working Group on Validated Methods for Optimization (May 27-31, 2002, with notes by George Corliss)

This is Vladik Kreinovich's comprehensive interval archive. It contains

Intervals and Probability Distributions
(by Dan Berleant)

The comprehensive archive on this subtopic

My page on uncertainty modeling

Bibliography of the old Freiburg Interval Library, a complete collection of over 2000 papers on interval analysis until 1987, until that time collected by Jürgen Garloff (garloff@fh-konstanz.de).

A bibtex version (1068KB; currently unavailable for downloading, but a copy of it can be searched) including more recent papers is being prepared by Nelson Beebe, who also has links to bibliographies on other Math/CS topics.

Karlsruhe Interval Bibliography

Reliable Computing: Table of Contents

VERSOFT: Verification software in MATLAB / INTLAB

(by Jiri Rohn)

includes an INTLAB primer, verified solvers for linear systems,
eigenvalues and eigenvectors, linear programming, polynomial zeros,
matrix functions, and the matrix equation A*X*B+C*X*D=F

b4m, Interval Arithmetic Toolbox for Matlab, based on PROFIL/BIAS (fast interval arithmetic)

Interval Arithmetic in Fortran 90

FI_LIB, fast interval library in ANSI-C, with C++ interface

FDLIBM (Freely Distributable LIBM) in C
from netlib

produces elementary function values with <1ulp relative error,
for machines that support IEEE 754 floating-point arithmetic
(readme file)

FADBAD and TADIFF C++ packages for performing automatic differentiation of functions implemented as C/C++ programs (including interval enclosures, based on PROFIL/BIAS)

XSC Software Homepage (free download of Pascal-XSC or C-XSC)

Online Interval Calculator (Hu and Hung)

libaa, affine arithmetic (Stolfi)

Fernando Alvarado, Madison, Wisconsin

Daniel Berleant (interval based arithmetic on random variables)

Gerd Bohlender, Karlsruhe, Germany

George F. Corliss, Milwaukee, Wisconsin

Tibor Csendes, Szeged, Hungary

Maarten van Emden, Victoria, Canada

R. Baker Kearfott, Lafayette, Louisiana

Vladik Kreinovich, El Paso, Texas

Ulrich Kulisch, Karlsruhe, Germany

and his interval crew

Wolfgang Kühn, ZIB, Berlin

Weldon Lodwick, Denver, Colorado

Rudolf Lohner, Karlsruhe, Germany

Early Interval Work of R. E. Moore (pdf files)

Marian Mrozek, Krakow , Poland

(computer-assisted proofs)

Rafi Muhanna

(intervals in finite element computations)

Knut Petras

(rigorous integration)

Andrzej Pownuk

(intervals in mechanical structures)

Dietmar Ratz, Karlsruhe, Germany

Siegfried Rump, Hamburg-Harburg, Germany

Jürgen Wolff von Gudenberg, Würzburg, Germany

Interval Computations/Reliable Computing (table of contents) and a local copy (upto 1995)

Reliable Computing (table of contents)

Solving interval quadratic equations (Dimitrova and Markov)

The Kepler Conjecture

local copy of the 2002 paper

local copy of the 2004 paper (containing a complete proof,
apart from the computer calculations)

Zonotopes for reduced wrapping (by Wolfgang Kühn)

Set Estimation using Constraints and Interval Analysis

uncertainty modeling

FMathL - Formal mathematical language

recent papers and preprints

global optimization

mathematics links

my home page (http://www.mat.univie.ac.at/~neum)

Arnold Neumaier (Arnold.Neumaier@univie.ac.at)