At the moment we have DegOpt objects that corresponds to evaluations
B3= (x I + x A) * (x I + x A)
B4= (x I + x A + xB3) * (x I + x A +xB3)
B5= (x I + x A + xB3+xB4) * (x I + x A +xB3 +xB4)
...
This is complete and one can represent any polynomial evaluation scheme in this way. However, many schemes are formulated in a slightly different way
B3= (x I + x A) * (x I + x A) + x I + xA
B4= (x I + x A + xB3) * (x I + x A +xB3) + xI +xA +xB3
B5= (x I + x A + xB3+xB4) * (x I + x A +xB3 +xB4) + xI +xA +xB3+xB4
...
One can always transform the second scheme to the first by incorporating the additional coefficients into the DegOpt-coefficients (basically adding multiples at appropriate places).
Since many schemes (e.g Horner, PS, Sastre, .. ) are easier to formulate in the second scheme, we could consider introducting ExtendedDegOpt which has three matrices (Ha,Hb,Hc,y) representing the second scheme. A function which transforms an extended to a standard DegOpt would make it much easier to use and implement other evaluations:
jarlebring
commented
6 months ago
At the moment we have
DegOptobjects that corresponds to evaluationsThis is complete and one can represent any polynomial evaluation scheme in this way. However, many schemes are formulated in a slightly different way
One can always transform the second scheme to the first by incorporating the additional coefficients into the
DegOpt-coefficients (basically adding multiples at appropriate places).Since many schemes (e.g Horner, PS, Sastre, .. ) are easier to formulate in the second scheme, we could consider introducting
ExtendedDegOptwhich has three matrices(Ha,Hb,Hc,y)representing the second scheme. A function which transforms an extended to a standard DegOpt would make it much easier to use and implement other evaluations: