Fast Enclosure of Matrix Polynomials
نویسنده
چکیده
A method for enclosing matrix polynomials is proposed. This method is applicable when the matrix is diagonalizable and supplies an interval matrix including the matrix polynomial. The computational cost of this method does not depend on the degree of the polynomial. Hence the proposed method is faster than previous approaches when the degree is large. Numerical results show the properties of this method.
منابع مشابه
Fast determination of the tensorial and simplicial Bernstein forms of multivariate polynomials and rational functions
Tests for speeding up the determination of the Bernstein enclosure of the range of a multivariate polynomial and a rational function over a box and a simplex are presented. In the polynomial case, this enclosure is the interval spanned by the minimum and the maximum of the Bernstein coe cients which are the coe cients of the polynomial with respect to the tensorial or simplicial Bernstein basis...
متن کاملGeneralized numerical ranges of matrix polynomials
In this paper, we introduce the notions of C-numerical range and C-spectrum of matrix polynomials. Some algebraic and geometrical properties are investigated. We also study the relationship between the C-numerical range of a matrix polynomial and the joint C-numerical range of its coefficients.
متن کاملSolving Linear Systems with Polynomial Parameter Dependency in the Reliable Analysis of Structural Frames
A wide range of scientific and engineering problems can be described by systems of linear algebraic equations involving uncertain model parameters. We consider such systems where the coefficients of the matrix and the right hand side are multivariate polynomials or rational functions of parameters varying within given intervals. A general-purpose parametric fixed-point iteration is combined wit...
متن کاملHigher rank numerical ranges of rectangular matrix polynomials
In this paper, the notion of rank-k numerical range of rectangular complex matrix polynomials are introduced. Some algebraic and geometrical properties are investigated. Moreover, for ϵ > 0; the notion of Birkhoff-James approximate orthogonality sets for ϵ-higher rank numerical ranges of rectangular matrix polynomials is also introduced and studied. The proposed denitions yield a natural genera...
متن کاملA Fast and Efficient On-Line Harmonics Elimination Pulse Width Modulation for Voltage Source Inverter Using Polynomials Curve Fittings
The paper proposes an algorithm to calculate the switching angles using harmonic elimination PWM (HEPWM) scheme for voltage source inverter. The algorithm is based on curve fittings of a certain polynomials functions. The resulting equations require only the addition and multiplication processes; therefore, it can be implemented efficiently on a microprocessor. An extensive angle error analysis...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Reliable Computing
دوره 18 شماره
صفحات -
تاریخ انتشار 2013