Displaying similar documents to “A Solver for Complex-Valued Parametric Linear Systems”

Introduction to the Maple Power Tool Intpakx

Krämer, Walter (2007)

Serdica Journal of Computing

Similarity:

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006 The Maple Power Tool intpakX [24] de nes Maple types for real intervals and complex disc intervals. On the level of basic operations, intpakX includes the four basic arithmetic operators, including extended interval division as an extra function. Furthermore, there are power, square, square root, logarithm and exponential functions, a set of standard...

Set arithmetic and the enclosing problem in dynamics

Marian Mrozek, Piotr Zgliczyński (2000)

Annales Polonici Mathematici

Similarity:

We study the enclosing problem for discrete and continuous dynamical systems in the context of computer assisted proofs. We review and compare the existing methods and emphasize the importance of developing a suitable set arithmetic for efficient algorithms solving the enclosing problem.

A novel interval arithmetic approach for solving differential-algebraic equations with VALENCIA-IVP

Andreas Rauh, Michael Brill, Clemens Günther (2009)

International Journal of Applied Mathematics and Computer Science

Similarity:

The theoretical background and the implementation of a new interval arithmetic approach for solving sets of differentialalgebraic equations (DAEs) are presented. The proposed approach computes guaranteed enclosures of all reachable states of dynamical systems described by sets of DAEs with uncertainties in both initial conditions and system parameters. The algorithm is based on VALENCIA-IVP, which has been developed recently for the computation of verified enclosures of the solution...

Interval analysis for certified numerical solution of problems in robotics

Jean-Pierre Merlet (2009)

International Journal of Applied Mathematics and Computer Science

Similarity:

Interval analysis is a relatively new mathematical tool that allows one to deal with problems that may have to be solved numerically with a computer. Examples of such problems are system solving and global optimization, but numerous other problems may be addressed as well. This approach has the following general advantages: (a) it allows to find solutions of a problem only within some finite domain which make sense as soon as the unknowns in the problem are physical parameters; (b) numerical...

Computing and Visualizing Solution Sets of Interval Linear Systems

Krämer, Walter (2007)

Serdica Journal of Computing

Similarity:

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006 The computation of the exact solution set of an interval linear system is a nontrivial task [2, 13]. Even in two and three dimensions a lot of work has to be done. We demonstrate two different realizations. The first approach (see [16]) is based on Java, Java3D, and the BigRational package [21]. An applet allows modifications of the matrix coefficients...

A verified method for solving piecewise smooth initial value problems

Ekaterina Auer, Stefan Kiel, Andreas Rauh (2013)

International Journal of Applied Mathematics and Computer Science

Similarity:

In many applications, there is a need to choose mathematical models that depend on non-smooth functions. The task of simulation becomes especially difficult if such functions appear on the right-hand side of an initial value problem. Moreover, solution processes from usual numerics are sensitive to roundoff errors so that verified analysis might be more useful if a guarantee of correctness is required or if the system model is influenced by uncertainty. In this paper, we provide a short...

A Mathematical Basis for an Interval Arithmetic Standard

Bohlender, Gerd, Kulisch, Ulrich (2010)

Serdica Journal of Computing

Similarity:

Basic concepts for an interval arithmetic standard are discussed in the paper. Interval arithmetic deals with closed and connected sets of real numbers. Unlike floating-point arithmetic it is free of exceptions. A complete set of formulas to approximate real interval arithmetic on the computer is displayed in section 3 of the paper. The essential comparison relations and lattice operations are discussed in section 6. Evaluation of functions for interval arguments is studied in section...