Refine
Document Type
- Conference Proceeding (24)
- Article (21)
- Part of a Book (1)
- Other Publications (1)
Keywords
- (Strict) sign-regularity (1)
- Bernstein coefficient (4)
- Bernstein coefficients (1)
- Bernstein function (1)
- Bernstein polynomial (7)
- Bernstein polynomials (1)
- Cauchon algorithm (6)
- Cauchon diagram (1)
- Cauchon matrix (1)
- Checkerboard ordering (4)
Institute
This paper considers intervals of real matrices with respect to partial orders and the problem to infer from some exposed matrices lying on the boundary of such an interval that all real matrices taken from the interval possess a certain property. In many cases such a property requires that the chosen matrices have an identically signed inverse. We also briefly survey related problems, e.g., the invariance of matrix properties under entry-wise perturbations.
Matrix methods for the computation of bounds for the range of a complex polynomial and its modulus over a rectangular region in the complex plane are presented. The approach relies on the expansion of the given polynomial into Bernstein polynomials. The results are extended to multivariate complex polynomials and rational functions.
Let A = [a_ij] be a real symmetric matrix. If f:(0,oo)-->[0,oo) is a Bernstein function, a sufficient condition for the matrix [f(a_ij)] to have only one positive eigenvalue is presented. By using this result, new results for a symmetric matrix with exactly one positive eigenvalue, e.g., properties of its Hadamard powers, are derived.