+- HP Forums (https://www.hpmuseum.org/forum)
+-- Forum: Not HP Calculators (/forum-7.html)
+--- Forum: Not remotely HP Calculators (/forum-9.html)
+--- Thread: (EL-5200/EL-9000) Polynomial interpolation and root finding (/thread-18021.html)
(EL-5200/EL-9000) Polynomial interpolation and root finding - robve - 02-10-2022 11:32 PM
This EL-5200 (1986) AER program is heavily "optimized" to barely fit within the limits of program size and complexity that EL-5200 AER programming permits. This was an interesting experiment to see if it was possible to combine easy (x,y) data point entry via STAT mode, perform polynomial interpolation, root finding and graphing. This shows what this tiny vintage 1986 machine can do, which is not much, compared to modern calculators. Only 3, 4 or 5 points can be interpolated.
LAGRANGE POLYNOMIAL INTERPOLATION AND ROOT FINDING WITH GRAPHING
For SHARP EL-5200/EL-9000
Select [STAT] then STAT 1 data store mode
Clear all data with [CA] or edit S[] data
Specify 3 to 5 (x,y) points to interpolate by repeating x,y M+
Draw the points of the polynomial:
[G(SD)] [AUTO] [DRAW]
Run the LAGRANGE program:
L [PRO] LAGRANGE [COMP]
[X<->Y] and [left]/[right] to select an x value
[X<->Y] to view y value
Press [SOLVE] repeatedly to find the roots
To zoom the graph:
[AUTO] 100 [ZOOM]
[X<->Y] to select an x value
[X<->Y] to view y value
[ZOOM]
[X<->Y] to select an x value
[X<->Y] to view y value
AER-I (and AER-II) program:
Code:
:LAGRANGE
M:➊Z[1]≠3→N→[➍◣]➋Z[1]≠4→N→[➎◣]➌➏◣
➊:S[1,1]⇒A␣S[1,2]⇒B␣S[1,3]⇒C␣A-B⇒F␣A-C⇒G␣B-C⇒H␣S[2,1]÷FG⇒S␣S[2,2]÷FH⇒T␣S[2,3]÷GH⇒U
➋:S[1,4]⇒D␣A-D⇒I␣B-D⇒J␣C-D⇒K␣S÷I⇒S␣T÷J⇒T␣U÷K⇒U␣S[2,4]÷IJK⇒V
➌:S[1,5]⇒E␣A-E⇒L␣B-E⇒M␣C-E⇒N␣D-E⇒O␣S÷L⇒S␣T÷M⇒T␣U÷N⇒U␣V÷O⇒V␣S[2,5]÷LMNO⇒W
➍:GRAPH S(X-B)(X-C)-T(X-A)(X-C)+U(X-A)(X-B)DRAW
➎:GRAPH S(X-B)(X-C)(X-D)-T(X-A)(X-C)(X-D)+U(X-A)(X-B)(X-D)-V(X-A)(X-B)(X-C)DRAW
➏:GRAPH S(X-B)(X-C)(X-D)(X-E)-T(X-A)(X-C)(X-D)(X-E)+U(X-A)(X-B)(X-D)(X-E)-V(X-A)(X-B)(X-C)(X-E)+W(X-A)(X-B)(X-C)(X-D)DRAW