We present a portable software package for finding all real roots of system nonlinear equations within region defined by bounds on the variables. Where practical, should find with mathematical certainty. Though based interval Newton methods, it is self-contained. It allows various control and output options does not require programming if are polynomials; structured further algorithmic research. Its practicality depend in simple way dimension or degree nonlinearity.

INTLIB is meant to be a readily available, portable, exhaustively documented interval arithmetic library, written in standard Fortran 77. Its underlying philosophy provide for operations aid efficiently transporting programs involving arithmetic. The model the BLAS package, basic linear algebra operations. library composed of elementary routines, function routines data and values, utility routines. can used with INTBIS (Algorithm 681), 90 module use define an type available from first author.

Certain cases in which the interval hull of a system linear equations can be computed inexpensively are outlined. We extend proposed technique Hansen and Rohn with formula that bounds solution set whose coefficient matrix $ {\bf{A}}= [ \underline A, \overline A ]$ is an H-matrix; when ${\bf A}$ centered about diagonal matrix, these smallest possible (i.e., then hull). Hansen's scheme also computes ${\bf{A}}{\bf{x}}={\bf{b}}=[{\underline b}, {\overline b}]$ such ${\bf{A}}$ inverse positive...

Interval Newton methods in conjunction with generalized bisection can form the basis of algorithms that find all real roots within a specified box ${\bf X} \subset {\bf R}^n $ system nonlinear equations $F(X) = 0$with mathematical certainty, even finite-precision arithmetic. In such methods, 0$ is transformed into linear interval $0 F(M) + F'}({\bf X})({\bf \bar - M)$ ; if arithmetic then used to bound solutions this system, resulting ${{\bf X}}$ contains system. The Gauss–Seidel method...

This paper addresses the task of reliably finding approximations to all solutions a system nonlinear equations within region defined by bounds on each individual coordinates. Various forms generalized bisection were proposed some time ago for this task. systematically compares such algorithms themselves, continuation methods, and hybrid steepest descent/quasi-Newton methods. A specific algorithm containing novel “expansion” “exclusion” steps is fully described, effectiveness these evaluated....

The authors present a step control for continuation methods that is deterministic in the sense (i) it computationally but rigorously verifies corrector iteration will converge to point on same curve as previous (i.e., predictor/corrector never jump across paths), and (ii) each predictor large possible, subject verification unique with given interval extension. performance data comparisons an approximate method (PITCON version 6.1). A comparison of plots obtained from both controls reveals...

The purpose of this paper is to study desirable properties binary search algorithms for isolating all solutions nonlinear systems equations <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper F left-parenthesis upper X right-parenthesis equals 0"> <mml:semantics> <mml:mrow> <mml:mi>F</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>X</mml:mi> stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow>...

A mathematical imaging method for simulating cortical surface potentials was introduced at recent neurosciences meetings [1a], [1b], [2] and applied to elucidate the neural origins of evoked responses in normal volunteers certain patient populations. This consists solution an inward harmonic continuation problem its effect is simulate data that has not been attenuated smeared by skull. technique (CIT) validated applying it artificially derived data. Pairs dipolar sources with different...

Abstract We explain the installation and use of GlobSol package for mathematically rigorous bounds on all solutions to constrained unconstrained global optimization problems, as well non-linear systems equations. This document should be both people with problems solve incorporating GlobSol's components into other or providing interfaces GlobSol. Keywords: nonconvex optimizationglobal optimizationGlobSolconstraint propagation AMS Subject Classification : 90C3065K0590C2665G20 Acknowledgements...

Interval arithmetic is useful in automatically verified computations , that is, which the algorithm itself rigorously proves answer must lie within certain bounds. In addition to rigor, interval also provides a simple and sometimes sharp method of bounding ranges functions for global optimization other tasks. Convenient use requires an data type programming language. Although various packages supply such type, previous ones are machine specific, obsolete, unsupported, languages than Fortran,...

An environment for general research into and prototyping of algorithms reliable constrained unconstrained global nonlinear optimization enclosure all roots systems equations, with or without inequality constraints, is being developed. This should be portable, easy to learn, use, maintain, sufficiently fast some production work. The motivation, design principles, uses, capabilities this are outlined. includes an interval data type, a symbolic form automatic differentiation obtain internal...