triang_Interpolation {polyMatrix}

Triangularization of a polynomial matrix by interpolation method

Description

The parameters point_vector, round_digits can significantly affect the result.

Usage

triang_Interpolation(
  pm,
  point_vector,
  round_digits = 5,
  eps = .Machine$double.eps^0.5
)

Arguments

pm

source polynimial matrix

point_vector

vector of interpolation points

round_digits

we will try to round result on each step

eps

calculation zero errors

Details

Default value of 'eps“ usually is enought to determintate real zeros.

In a polynomial matrix the head elements are the first non-zero polynomials of columns. The sequence of row indices of this head elements form the shape of the polynomial matrix. A polynomial matrix is in left-lower triangular form, if this sequence is monoton increasing.

This method offers a solution of the triangulrization by the Interpolation method, described in the article of Labhalla-Lombardi-Marlin (1996).

Value

Tranfortmaiton matrix