Interval Methods for Systems of Equations
Encyclopedia of Mathematics and its Applications 37,
Cambridge Univ. Press, Cambridge 1990
(out of print)
R.B. Kearfott, M.T. Nakao, A. Neumaier, S.M. Rump, S.P. Shary, and P. van Hentenryck, Standardized notation in interval analysis
Slides on robotics applications
A. Neumaier, Certified error bounds for uncertain elliptic equations
A. Neumaier, Computer-assisted proofs
A. Neumaier and A. Pownuk, Linear systems with large uncertainties, with applications to truss structures
D. Daney, Y. Papegay and A. Neumaier, Interval methods for certification of the kinematic calibration of parallel robots
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.
The enclosure of solutions of parameter-dependent systems of
In: Reliability in Computing (ed. by R.E. Moore).
Acad. Press, San Diego 1988, pp. 269-286.
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)
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 (firstname.lastname@example.org).
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
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)
BLAS Technical Workshop 1995
BLAS Technical Workshop 1996
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
Oscar E. Lanford III
Weldon Lodwick, Denver, Colorado
Rudolf Lohner, Karlsruhe, Germany
Early Interval Work of R. E. Moore (pdf files)
Marian Mrozek, Krakow , Poland
(intervals in finite element computations)
(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)
Modal Interval Analysis
Set Estimation using Constraints and Interval Analysis
Arnold Neumaier (Arnold.Neumaier@univie.ac.at)