510 Mathematik
Refine
Year of publication
- 2018 (8) (remove)
Document Type
- Conference Proceeding (5)
- Article (2)
- Doctoral Thesis (1)
Language
- English (8)
Keywords
- Bernstein Basis (1)
- Bernstein polynomial (1)
- Cauchon algorithm (3)
- Cauchon diagram (1)
- Cauchon matrix (1)
- Checkerboard partial ordering (1)
- Complex interval (1)
- Complex polynomial (1)
- Control Theory (1)
- Cyclic sign variation (1)
Institute
In 1970, B.A. Asner, Jr., proved that for a real quasi-stable polynomial, i.e., a polynomial whose zeros lie in the closed left half-plane of the complex plane, its finite Hurwitz matrix is totally nonnegative, i.e., all its minors are nonnegative, and that the converse statement is not true. In this work, we explain this phenomenon in detail, and provide necessary and sufficient conditions for a real polynomial to have a totally nonnegative finite Hurwitz matrix.
Further applications of the Cauchon algorithm to rank determination and bidiagonal factorization
(2018)
For a class of matrices connected with Cauchon diagrams, Cauchon matrices, and the Cauchon algorithm, a method for determining the rank, and for checking a set of consecutive row (or column) vectors for linear independence is presented. Cauchon diagrams are also linked to the elementary bidiagonal factorization of a matrix and to certain types of rank conditions associated with submatrices called descending rank conditions.
This thesis considers bounding functions for multivariate polynomials and rational functions over boxes and simplices. It also considers the synthesis of polynomial Lyapunov functions for obtaining the stability of control systems. Bounding the range of functions is an important issue in many areas of mathematics and its applications like global optimization, computer aided geometric design, robust control etc.