polyMatrix (version 0.3.1)

triang_Interpolation: 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

Value

Tranfortmaiton matrix

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).

Examples

# NOT RUN {
A <- polyMgen.d(3,2,ch2pn(c("x-1","2","0","x^2-1","2*x+2","3")))

triang_Interpolation(A, -2:2)
# 0.79057 - 0.31623*x + 0.15812*x^2   -0.57735 - 0.57735*x
# 0.47434 - 0.15811*x - 1e-05*x^2     0.57735

triang_Interpolation(A, -10:10)
# 0.79057 - 0.3161*x + 0.15803*x^2   0.25574 - 0.3541*x - 0.60984*x^2
# 0.47448 - 0.15807*x                -0.25574 + 0.60984*x
# }