plot(data,a,b,c)

6419480a-ffa7-4398-984c-4889a6962790 17 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

plot(data,a,b,c)

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

Lobatto Polynomials & Polyroots

Legendre  setup 6179 needs "local assignment" n x L 1 - (k^2 n * 2 k * - (! (x n 2 k * -^* (* 2 n^k! (* n k - (! (n 2 k * - (! (* (* / (k 0 n 2 / Floor sum 11 line :

x λ 11 - x ≤ (x 1 ≤ (& cases :

n x Lobatto n 1 - x L x diff :

Polyroots Vector

optimiz NONE 10 x Lobatto x expand maple 70931694131085692882303761517125 / 312099454176776532 x 2^* 2882303761517125 / - 10143232260745234014 x 4^* 14411518807585625 / + 4057292904298093044 x 6^* 2882303761517125 / - 2463356406180984873 x 8^* 2882303761517125 / +

v 70931694131085692882303761517125 / 03120994541767765322882303761517125 / - 01014323226074523401414411518807585625 / 040572929042980930442882303761517125 / - 024633564061809848732882303761517125 / 91 mat :

Lobatto system [Wr] ... plots roots r v polyroots : r r eval : roots r r 0 * augment : roots roots . 14 black plot : ρ 1 - r 1 stack : 51 line

n 10 :

roots 10 x Lobatto x λ * 2 1 sys

i 1 ρ rows range W i el 2 n n 1 - (* n 1 - ρ i el L (2^* / : Wr ρ W augment : 21 line for

x f x 1 - 1 int W 1 el 1 - f * W i el x i el f * i 2 n 1 - sum + W n el 1 f * + ≡

Sanity Abaramowitz 
P. 920 ... n = 10 Wr 1 - 0.0222222222 0.1652789577 - 0.3275397612 0.1652789577 0.3275397612 0.4779249498 - 0.2920426837 0.4779249498 0.2920426837 0.7387738651 - 0.2248893421 0.7387738651 0.2248893421 0.9195339082 - 0.1333059909 0.9195339082 0.1333059909 1 0.0222222222 102 mat

Legendre  setup 6179 needs "local assignment" n x L 1 - (k^2 n * 2 k * - (! (x n 2 k * -^* (* 2 n^k! (* n k - (! (n 2 k * - (! (* (* / (k 0 n 2 / Floor sum 11 line :

Lobatto explorer ... Export

n x Lobatto n 1 - x L x diff :

j 10 : n 1 j range Lob n el n x Lobatto : for 21 line

select/collect Lob 5 el 5 x * 3 - 7 x 2^* + (* 2 /

eval SYMBOLIC view all x Lobatto Lob :

x λ 11 - x ≤ (x 1 ≤ (& cases :

j 10 :

ρoots x Lobatto j el x 1 - 1 solve : ρoots ρoots eval : roots ρoots ρoots 0 * augment : roots roots . 14 black plot : 41 line

roots x Lobatto j el x λ * 1 2 1 2 - 2 2 mat 3 1 sys

ρoots 0.9195 - 0.7388 - 0.4779 - 0.1653 - 0.1653 0.4779 0.7388 0.9195 81 mat

Lobatto polyroots otherwise . . . for export . . . User Applications

]]> plot(data,a,b,c)

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

Legendre  setup 6179 needs "local assignment" n x L 1 - (k^2 n * 2 k * - (! (x n 2 k * -^* (* 2 n^k! (* n k - (! (n 2 k * - (! (* (* / (k 0 n 2 / Floor sum 11 line :

n x Lobatto n 1 - x L x diff :

j 10 : n 1 j range Lob n el n x Lobatto : for 21 line

select/collect Lob 5 el 5 x * 3 - 7 x 2^* + (* 2 /

n 10 :

eval SYMBOLIC view all x Lobatto Lob :

x N n x Lobatto x expand maple : x N x N op maple : x 1 : v x N : 12 mat 31 line

i 1 v rows range n 2 mod 0 ≡ L 2 i * 1 - el v i el : L 2 i * el v i el : if for

r L polyroots : r r eval : 21 sys

'n' even

Plot roots of Lobatto roots r r 0 * augment : roots roots . 14 black plot : 21 line

'n' odd

roots n x Lobatto 2 1 sys

L 2.4609 0 108.2813 - 0 703.8281 0 1407.6562 - 0 854.6484 91 mat

r 0.165278957666 - 0.165278957666 0.477924949809 - 0.477924949809 0.738773865106 - 0.738773865106 0.919533908167 - 0.919533908167 81 mat