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Pointwise numerical index determination of unstructured DAEs
Author(s) -
Lamour René
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110399
Subject(s) - pointwise , measure (data warehouse) , realization (probability) , matrix (chemical analysis) , dimension (graph theory) , sequence (biology) , index (typography) , mathematics , component (thermodynamics) , numerical analysis , algorithm , computer science , mathematical optimization , mathematical analysis , pure mathematics , data mining , statistics , physics , materials science , genetics , biology , world wide web , composite material , thermodynamics
The index of a DAE is a measure of the expected difficulties arising when solving it. The tractability index concept determines the index without knowing any solution. It is based on a matrix sequence with matrices of the same dimension as the DAE under consideration. For the numerical realization of the matrix sequence it is advantageous to use so‐called widely orthogonal projectors and to compute derivatives by means of algorithmic differentiation (AD) because of the higher accuracy. The presented method of numerical index determination may become a basic component on the way to a robust index monitor. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)