companion: Generate Companion Matrices

In wrathematics/pbdDMAT: 'pbdR' Distributed Matrix Methods

Generate Companion Matrices

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} + \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.

Value

Returns a matrix or a distributed matrix.

wrathematics/pbdDMAT documentation built on Oct. 2, 2024, 2:56 p.m.