Triangularization of a polynomial matrix by interpolation method
The parameters 'point_vector', 'round_digits' can significantly affect the result.
triang_Interpolation( pm, point_vector, round_digits = 5, eps = .Machine$double.eps^0.5 )
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 |
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).
Tranfortmaiton matrix
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*xPlease choose more modern alternatives, such as Google Chrome or Mozilla Firefox.