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Numerical issues and computational problems in algebraic control theory

Mitrouli, M. (1991). Numerical issues and computational problems in algebraic control theory. (Unpublished Doctoral thesis, City, University of London)


The work of this thesis concerns computational issues arising from various fields of Algebraic Control Theory. Efficient algorithms covering the following classes of problems are developed.

(i) Exterior Algebra Computations: For given matrices [Please see formulas inside thesis] algorithms achieving the computation of [Please see formulas inside thesis] are formulated. An algorithm for the evaluation of Plucker matrices is also proposed. Most of these algorithms are used in the development of a unifying numerical algorithm for the solution of the Determinantal Assignment Problem.

(ii) Numerical Techniques for handling nonqeneric computations: Several numerical tools for the diagnosis of certain properties in an "almost sense", and the definition of procedures attaining the termination of algorithms are developed.

(iii) Evaluation of the Greatest Common Divisor of polynomials: A new numerical algorithm for the evaluation of the greatest common divisor of any set of polynomials is formulated.

(iv) Almost Zero Computations: Algorithms achieving the evaluation of the Prime almost zero of a polynomial set and the computation of the zero radius are given. Useful comments about the achievement of improved bounds for the zero-trapping region are also presented.

Publication Type: Thesis (Doctoral)
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Departments: School of Science & Technology > Computer Science
School of Science & Technology > School of Science & Technology Doctoral Theses
Doctoral Theses
Text - Accepted Version
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