a566c3a3-3a10-4eb2-aa13-88528cbb92d0 5 4 5 decimal

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

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 :

start n stop range algo u start stop start n + range vectorize : out u j el j 1 range sum : 21 line :

Adjust stop wrt 'n' ... or large enough start 0 : n 1.5 : stop 100 : 13 mat

explore the rangebility range 120 range :

Collect the system u start stop start n + range vectorize : Sum start n stop range algo vectorize : cumulative u range el Sum augment : data cumulative . 12 black plot : 41 sys

cumulative 00 1.5 1.5 3 4.5 4.5 9615 7.5 22.5 9 31.5 10.5 421254 13.5 67.5 15 82.5 16.5 9918117 19.5 136.5 21 157.5 22.5 18024204 25.5 229.5 27 256.5 28.5 285202 mat

recast for convenience Σ cumulative :

j cumul out Σ j 2 el Σ j 1 + 1 el + (: j 1 + out augment 21 line :

j 15 :

j cumul 1618012 mat

myΣ Σ j 1 + 1 el Σ j 1 + 2 el 12 mat + 20 blue plot :

data cumulative myΣ 3 1 sys

Σ j 1 + 1 el Σ j 1 + 2 el 12 mat 22.5 18012 mat

X cumulative 1 col : Y cumulative 2 col : 21 line

x φ 1 x x 2^31 mat :

Cholesky companion solver j 1 x φ length range i 1 X length range M i j el X i el φ j el : for for Φ M transpose M * : d M transpose Y * : 12 mat b Φ 1 -^eval d * : 31 line

b 4.61222 1010 -^* - 0.5 0.333333 31 mat

M transpose M * not commutative ≡

M transpose Y * not commutative ≡

recast this strictly parabolic b 0 0.5 13 / 31 mat :

<= recast the scalar model x fit b x φ * :

data x fit 2 1 sys

x fit x 32 x * + (* 6 /