Interpolation Equation - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: HP Calculators (and very old HP Computers) (/forum-3.html) +--- Forum: General Forum (/forum-4.html) +--- Thread: Interpolation Equation (/thread-22006.html) |
Interpolation Equation - MNH - 07-08-2024 01:23 AM The following is from my online Hydraulics and Hydrology class. The required elevation for a volume of 0.46 acre-ft. is somewhere between 74 ft. and 75 ft. The accumulated volumes are therefore between 0.39 acre-ft. and 0.65 acre-ft. Use the interpolation equation to figure it out. I never heard of the term interpolation equation. Is it the same as linear regression? I found y - y1 = [(y2 - y1) / (x2 - x1)] (x - x1) on Wikipedia. I could easily write something for my HP 48G to crunch these numbers, but I figure there's already something on the HP 48G to do the same thing. There always seems to be a semantics issue involved when trying to figure out how to do something like this. My class learning module gives an example of calculating this using Microsoft Excel, but since I can't read the blurry text in the formula bar, I'm resorting to doing the math on my calculator. RE: Interpolation Equation - Namir - 07-08-2024 01:29 AM You already have the formula, and should be easy to write in in RPL. you need to input x1,y1,x2,y2,and x from the stack and sore them in named variables. The you write an rPL code for the equation using your named variables. Simple! Namir RE: Interpolation Equation - SlideRule - 07-08-2024 01:33 AM [attachment=13696] BEST! SlideRule RE: Interpolation Equation - Thomas Klemm - 07-08-2024 02:09 PM You could use linear regression: [[.39 74] [.65 75]] STOΣ .46 PREDY 74.2692307692 RE: Interpolation Equation - KeithB - 07-08-2024 02:43 PM There are a number of interpolation formulas depending on the number of points you use to interpolate with: Check out section 25.2 of Handbook of Mathematical functions by Abramowitz and Stegun. https://personal.math.ubc.ca/~cbm/aands/abramowitz_and_stegun.pdf RE: Interpolation Equation - Namir - 07-08-2024 03:00 PM (07-08-2024 02:09 PM)Thomas Klemm Wrote: You could use linear regression: Cool! RE: Interpolation Equation - Gil - 07-08-2024 06:12 PM You could use this program INTERP, that works for n (n not too big) points : it finds the exact Polynom that goes through the n points. Code:
RE: Interpolation Equation - Thomas Klemm - 07-08-2024 07:32 PM (07-08-2024 02:09 PM)Thomas Klemm Wrote: STOΣ For those unfamiliar: (08-02-2022 11:54 AM)Thomas Klemm Wrote: I was pleasantly surprised by the following: RE: Interpolation Equation - Gil - 07-08-2024 07:46 PM It works for any variable : [LeftShift] XXxxxx→ 'XXxxxx' STO [RightShift] XXxxxx → 'XXxxxx' RCL RE: Interpolation Equation - Thomas Klemm - 07-08-2024 08:13 PM (07-08-2024 07:46 PM)Gil Wrote: It works for any variable There’s a difference between [ΣDAT] in the VAR menu and [ΣDAT] in the STAT DATA menu. You will notice it if you press the [LeftShift] key within a program: Code: « 'ΣDAT' STO » RE: Interpolation Equation - Thomas Klemm - 07-08-2024 08:19 PM (07-08-2024 01:23 AM)MNH Wrote: Is it the same as linear regression? (02-10-2024 06:26 PM)Thomas Klemm Wrote: For just two points \(P_1 = (x_1, y_1)\) and \(P_2 = (x_2, y_2)\) we want to solve the following linear system of equations: RE: Interpolation Equation - PedroLeiva - 07-09-2024 10:37 AM I would like to check my comprehension and test the formulas, could you please give me an example? Thank you in advance. Pedro RE: Interpolation Equation - Albert Chan - 07-09-2024 11:09 AM Linear regression line minimize Mean Squared Error (MSE) For 2 points, it is the same as the secant line. (MSE = 0) Proof: from secant line, we can get regression line formula. a * x1 + b = y1 ... (1) a * x2 + b = y2 ... (2) (1) * x1 + (2) * x2: a * (x1²+x2²) + b * (x1+x2) = (y1*x1 + y2*x2) ... (3) (1) + (2): a * (x1+x2) + 2 * b = (y1+y2) ... (4) (3) and (4) are exactly n=2 linear regression formula. RE: Interpolation Equation - Thomas Klemm - 07-09-2024 12:13 PM (07-09-2024 10:37 AM)PedroLeiva Wrote: could you please give me an example? This is the example given by MNH: HP-15C f CLEAR Σ 74 ENTER .39 Σ+ 75 ENTER .65 Σ+ .46 f ŷ,r 74.26923077 HP-42S CLΣ 74 ENTER .39 Σ+ 75 ENTER .65 Σ+ .46 FCSTY 74.2692307692 RE: Interpolation Equation - PedroLeiva - 07-09-2024 12:22 PM Thanks to both, Albert and Thomas. I have just found the formula and example in "HP25 Application Programs". If X1= 7.3, Y1= 1.9879; x2= 7.4, Y2= 2.0015; for Xn= 7.37, then Yn= 1.9974. The program only takes 16 steps (pages 85-86) RE: Interpolation Equation - Thomas Klemm - 07-09-2024 12:51 PM (07-09-2024 12:22 PM)PedroLeiva Wrote: I have just found the formula and example in "HP25 Application Programs". We've been there: Lagrangian Interpolation Post: #20 RE: Interpolation Equation - PedroLeiva - 07-09-2024 01:00 PM Yes, you are right. It was in March 2019, I was forgotten, sorry RE: Interpolation Equation - Johnh - 07-09-2024 11:27 PM That simple use of linear regression with two points is really useful! Actually it may be more useful in day-to-day engineering than the more common use of LR with multiple points. Thanks! And it's so simple that there's no point in making a dedicated program. Today's example for me in structural design: Design standards give us wind pressure coefficients at various building heights. To get the values at intermediate heights, we interpolate from the nearest values above and below. |