Verification of Invertibility of Complicated Functions over Large Domains
AbstractA new method to decide the invertibility of a given high-dimensional
function over a domain is presented. The problem arises in the field
of verified solution of differential algebraic equations (DAEs)
related to the need to perform projections of certain constraint
manifolds over large domains. The question of invertibility is
reduced to a verified linear algebra problem involving first
partials of the function under consideration. Different from
conventional approaches, the elements of the resulting matrices are
Taylor models for the derivatives of the functions.
The linear algebra problem is solved based on Taylor model methods,
and it will be shown the method is able to decide invertibility with
a conciseness that often goes substantially beyond what can be
obtained with other interval methods. The theory of the approach is
presented. Comparisons with three other interval-based methods are
performed for practical examples, illustrating the applicability of
the new method.
J. Hoefkens, M. Berz, Reliable Computing 8(1) (2002) 1-16
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