Add Horner scheme

[schillic]

This is basically the implementation by @mforets here.

(I observed that at some point the exponential remainder starts growing again, but this is not a problem of this PR → #145.)

julia> m = IntervalMatrix([-1.1..0.9 -4.1.. -3.9; 3.9..4.1 -1.1..0.9]);

julia> for K in [4, 6, 8, 20, 30]
           H = horner_scheme(m, K)
       end
K: 4
H: Interval{Float64}[[-6.59711, 16.4024] [-4.60191, 16.6734]; [-16.6734, 4.60191] [-6.59711, 16.4024]]
R: Interval{Float64}[[-107.653, 107.653] [-107.653, 107.653]; [-107.653, 107.653] [-107.653, 107.653]]
result: Interval{Float64}[[-114.25, 124.055] [-112.255, 124.326]; [-124.326, 112.255] [-114.25, 124.055]]
diam: [238.30443375030262 236.58025875030262; 236.58025875030262 238.30443375030262]
K: 6
H: Interval{Float64}[[-16.098, 11.2656] [-15.8269, 12.8829]; [-12.8829, 15.8269] [-16.098, 11.2656]]
R: Interval{Float64}[[-48.5097, 48.5097] [-48.5097, 48.5097]; [-48.5097, 48.5097] [-48.5097, 48.5097]]
result: Interval{Float64}[[-64.6077, 59.7752] [-64.3365, 61.3926]; [-61.3926, 64.3365] [-64.6077, 59.7752]]
diam: [124.38282465585809 125.72902259752476; 125.72902259752476 124.38282465585809]
K: 8
H: Interval{Float64}[[-16.9448, 18.0497] [-15.3549, 18.6421]; [-18.6421, 15.3549] [-16.9448, 18.0497]]
R: Interval{Float64}[[-14.8526, 14.8526] [-14.8526, 14.8526]; [-14.8526, 14.8526] [-14.8526, 14.8526]]
result: Interval{Float64}[[-31.7974, 32.9023] [-30.2075, 33.4947]; [-33.4947, 30.2075] [-31.7974, 32.9023]]
diam: [64.69952648085506 63.70205977610654; 63.70205977610654 64.69952648085506]
K: 20
H: Interval{Float64}[[-18.5586, 18.6197] [-17.1485, 19.3592]; [-19.3592, 17.1485] [-18.5586, 18.6197]]
R: Interval{Float64}[[-2.77417e-05, 2.77417e-05] [-2.77417e-05, 2.77417e-05]; [-2.77417e-05, 2.77417e-05] [-2.77417e-05, 2.77417e-05]]
result: Interval{Float64}[[-18.5586, 18.6197] [-17.1485, 19.3592]; [-19.3592, 17.1485] [-18.5586, 18.6197]]
diam: [37.17821738633965 36.507641933692234; 36.507641933692234 37.17821738633965]
K: 30
H: Interval{Float64}[[-18.5586, 18.6197] [-17.1485, 19.3592]; [-19.3592, 17.1485] [-18.5586, 18.6197]]
R: Interval{Float64}[[-452.145, 452.145] [-452.145, 452.145]; [-452.145, 452.145] [-452.145, 452.145]]
result: Interval{Float64}[[-470.704, 470.765] [-469.294, 471.504]; [-471.504, 469.294] [-470.704, 470.765]]
diam: [941.4678769593615 940.7973015555041; 940.7973015555041 941.4678769593615]

[mforets]

Later it would be nice to export exp which combines the horner evaluation with the scaling and squaring method, as in section 4.3 of the paper.

[schillic]

Later it would be nice to export exp which combines the horner evaluation with the scaling and squaring method

I updated #120.