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pbdDMAT (version 0.2-3)

Companion: Generate Companion Matrices

Description

Methods for constructing companion matrices of an n-degree polynomial.

Usage

companion(coef, type="matrix", ..., bldim=.BLDIM, ICTXT=.ICTXT)

Arguments

coef
Vector of polynomial coefficients, listed in increasing order (by index; see details below).
type
"matrix" or "ddmatrix".
...
Additional arguments.
bldim
blocking dimension.
ICTXT
BLACS context number.

Value

  • Returns a matrix or a distributed matrix.

Details

For a degree n polynomial, $x^n + a_{n-1}x^{n-1} + \dots + a_1x + a_0$ its associated companion matrix is a matrix of the form $\left[\begin{array}{cccccc} 0 & 0 & 0 & \dots & 0 & -a_0\ 1 & 0 & 0 & \dots & 0 & -a_1\ 0 & 1 & 0 & \dots & 0 & -a_2\ \vdots & \vdots & \vdots & \ddots & \vdots & \vdots\ 0 & 0 & 0 & \dots & 1 & -a_{n-1} \end{array}\right]$ In the function call, we assume that the argument 'coef' is ordered from $a_0$ to $a_{n-1}$. NOTE that we assume that the leading coefficient is 1.