companion: Generate Companion Matrices

In pbdDMAT: 'pbdR' Distributed Matrix Methods

Description

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

Usage

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

Details

For a degree n polynomial,

x^n + a_{n-1}x^{n-1} + … + a_1x + a_0

its associated companion matrix is a matrix of the form

≤ft[\begin{array}{cccccc} 0 & 0 & 0 & … & 0 & -a_0\\ 1 & 0 & 0 & … & 0 & -a_1\\ 0 & 1 & 0 & … & 0 & -a_2\\ \vdots & \vdots & \vdots & \ddots & \vdots & \vdots\\ 0 & 0 & 0 & … & 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.

Value

Returns a matrix or a distributed matrix.

pbdDMAT documentation built on May 1, 2019, 6:34 p.m.