Lagrangian Interpolation
12-18-2013, 06:04 AM (This post was last modified: 01-17-2014 05:18 AM by Namir.)
Post: #1
 Namir Senior Member Posts: 693 Joined: Dec 2013
Lagrangian Interpolation
Langrangian Interpolation of 3 points

Usage

A program prompts you to enter 3 points and the
interpolated x

Enter y1 and the x1 at first prompt
Enter y2 and the x2 at second prompt
Enter y3 and the x3 at third prompt
Enter xint at fourth prompt
Note calculator displays 1, 2, 3 at the first, second,
and thir dprompt

B program prompts you to enter the interpolated x

Program calculates and display the value of the interpolated Y.

Algorithm

Code:
INPUT N, array X(1..N), Y(1..N), and Xint Yint = 0 FOR I = 1 TO N   Product = Y(I)   FOR J = 1 to N     IF I <> J THEN       Product = Product * (Xint - X(J)) / (X(I) - X(J))     ENDIF   NEXT J   Yint = Yint + Product NEXT I Show Yint

Memory Map

R00 = x1
R01 = x2
R02 = X3
R03 = y1
R04 = y2
R05 = y3
R06 = x
R07 = y
R08 = Product
R09 = used
A = I for X(I)
B = J for X(J)
C = I for Y(I)

Source Code

Code:
 1 LBL A 2 1 3 R/S        # enter Y1 and X1 4 STO 0 5 x<>y 6 STO 3 7 2 8 R/S        # enter Y2 and X2 9 STO 1 10 x<>y 11 STO 4 12 3 13 R/S        # enter Y2 and X3 14 STO 2 15 x<>y 16 STO 5 17 R/S        # enter Xint 18 LBL B 19 STO 6 20 2 21 STO B        # set J for X(J) 22 5 23 STO C        # set I for Y(I) 24 0 25 STO 7        # y = 0 26 LBL 0        # outer loop starts 27 RCL C 28 GSB 9 29 STO 8 30 2 31 STO A        # set I fo X(I) 32 LBL 1        # inner loop starts 33 RCL A 34 RCL B 35 x=y?        if I = J the skip iteration 36 GTO 2 37 RCL 6 38 RCL A 39 GSB 9 40 STO 9 41 - 42 RCL B  43 GSB 9 44 RCL 9 45 - 46 / 47 STO* 8        # update product 48 LBL 2 49 RCL A 50 1 51 - 52 STO A 53 x>0? 54 GTO 1        # inner loop ends 55 x=0? 56 GTO 1 57 RCL 8 58 STO+ 7 59 RCL B 60 1 61 - 62 STO B 63 RCL C 64 1 65 - 66 STO C 67 RCL B 68 x>0? 69 GTO 0        # outer loop ends 70 x=0? 71 GTO 0 72 RCL 7 73 R/S 74 GTO B 75 LBL 9        # INDIRECT ADDRESS 76 STO I 77 RDN 78 RCL (I) 79 RTN
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 Messages In This Thread Lagrangian Interpolation - Namir - 12-18-2013 06:04 AM RE: Lagrangian Interpolation - bshoring - 03-05-2015, 05:17 AM RE: Lagrangian Interpolation - PedroLeiva - 03-05-2015, 09:33 PM RE: Lagrangian Interpolation - bshoring - 03-07-2015, 11:49 PM RE: Lagrangian Interpolation - PedroLeiva - 03-09-2015, 03:37 AM RE: Lagrangian Interpolation - Thomas Klemm - 03-08-2015, 06:02 AM RE: Lagrangian Interpolation - Thomas Klemm - 03-08-2015, 07:58 PM RE: Lagrangian Interpolation - bshoring - 03-09-2015, 03:30 AM RE: Lagrangian Interpolation - Thomas Klemm - 03-09-2015, 09:36 AM RE: Lagrangian Interpolation - bshoring - 03-09-2015, 09:50 PM RE: Lagrangian Interpolation - Thomas Klemm - 03-11-2015, 08:04 AM RE: Lagrangian Interpolation - bshoring - 03-13-2015, 05:33 AM RE: Lagrangian Interpolation - Newton Polynomial - bshoring - 04-04-2015, 07:40 PM RE: Lagrangian Interpolation - Thomas Klemm - 03-09-2019, 07:08 PM RE: Lagrangian Interpolation - PedroLeiva - 03-14-2019, 03:55 PM RE: Lagrangian Interpolation - Thomas Klemm - 03-14-2019, 05:56 PM RE: Lagrangian Interpolation - PedroLeiva - 03-14-2019, 07:22 PM RE: Lagrangian Interpolation - Thomas Klemm - 03-14-2019, 07:58 PM RE: Lagrangian Interpolation - PedroLeiva - 03-14-2019, 08:12 PM

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