89f553ed-5942-4367-abf4-3f43edc5e6da 4 4 5 decimal

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

"RootDichotomy"  is a robust companion. # Φ a b ε D RootDichotomy xn b a + (2 / : n 0 : xn Φ abs ε ≥ xn Φ a Φ * 0 ≤ b xn : a xn : if xn b a + (2 / : n n 1 + : 31 line while xn 51 line :

"RootSecant" is viable  => guess wisely tial/error Φ a b ε X Root Secant us 1 el ε : us 2 el b b Φ a b - (* a Φ b Φ - / - : i 2 : us i 1 + el us i el us i el Φ us i 1 - el us i el - (* us i 1 - el Φ us i el Φ - / - : us i el us i 1 - el - abs ε ≥ us i 1 + el us i el us i el Φ us i 1 - el us i el - (* us i 1 - el Φ us i el Φ - / - : i i 1 + : 21 line while us us rows row 1 el 71 line :

r 0 x mwbesselj x 030 solve :

x f 0.00625 x * :

x B 0 x mwbesselj :

0 x mwbesselj x f 2 1 sys

r 2.404826 5.520078 8.653728 11.791534 14.930918 18.071064 21.211637 24.352472 27.493479 91 mat

sanity checked up to mwbesselj(0,40) 040 mwbesselj 0.007366890584237

"roots" fails ... mwbesselj(0,x) does NOT
have symbolic derivative(s) diff(▪,▪) exact 0 x mwbesselj x 1 roots :

r Clear 1

ε 1015 -^:

x Φ 0 x mwbesselj :

braket wisely
rootDichotomy
... etc. r x Φ 2.3 2.5 ε D x Φ 5.4 5.6 ε D x Φ 8.6 8.7 ε D x Φ 11.7 11.9 ε D x Φ 14.5 15.5 ε D 51 mat : 2.40482555769577 5.52007811028631 8.65372791291101 11.7915344390143 14.9309177084878 51 mat

Guesstimate for RootSecant X(Φ,a,b,ε) x x f - B x 020 solve 2.42 5.5548 8.7082 11.8657 15.0248 18.1847 61 mat

x Φ x B x f - (eval :

Intersect Φ 23 ε X Φ 56 ε X Φ 89 ε X Φ 1113 ε X Φ 1415 ε X Φ 1819 ε X 61 mat :

Intersect 2.37638206105862 5.6245547834828 8.45992250470978 12.1286151984414 14.4845295371415 18.7609539221604 61 mat