Generalized Characteristic Polynomials
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A Method of Generalized Characteristics
Author: Marc A. Berger
language: en
Publisher: American Mathematical Soc.
Release Date: 1982
The classical and Brownian methods of characteristics are generalized to analyze evolution equations of arbitrary order. Calculi of higher orders, analogous to first order classical calculus and second order Ito calculus, are constructed. Solutions of differential equations in the calculi become characteristic propagators of higher order partial differential equations. The solutions of these partial differential equations are then represented as averages of random samples of initial data based on these characteristic flows, in a general sense.
Generalized Characteristic Polynomials
Author: University of California, Berkeley. Computer Science Division
language: en
Publisher:
Release Date: 1988
We generalize the notion of characteristic polynomial for a system of linear equations to systems of multivariate polynomial equations. The generalizaiton is natural in the sense that it reduces to the usual definition when all the polynomials are linear. Whereas the constant coefficient ofthe general characteristic polynomial is the resultant of the system. This construction is applied to solve a traditional problem with efficient methods for solving systems of polynomials, even in the presence of infinitely many solutions "at infinity". We give a single-exponential time method for finding all the isolated solution points of a system of polynomials, even in the presence of infinitely many solutions at infinity or elsewhere.
Matrix Analysis and Applications
Author: Xian-Da Zhang
language: en
Publisher: Cambridge University Press
Release Date: 2017-10-05
The theory, methods and applications of matrix analysis are presented here in a novel theoretical framework.