(41C) and (42S) Arithmetic-Geometric Mean
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07-26-2020, 07:50 PM
Post: #1
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(41C) and (42S) Arithmetic-Geometric Mean
Arithmetic-Geometric Mean
The program AGM calculates the arithmetic-geometric mean of two positive integers x and y. As the graphic above suggests, an iterative process is used to find the AGM, computing both the arithmetic mean and geometric mean until the two means converge. a0 = x g0 = y Repeat: Arithmetic Mean: a1 = (a0 + g0)/2 Geometric Mean: g1 = √(a0 * g0) Transfer new to old: a0 = a1, g0 = g1 Until |a1 - g1| < tolerance You can set the tolerance as low as you want. The programs presented on this blog set tolerance at 10^(-10) (1E-10), to fit the calculator's display. HP 41C Program: AGM 01 LBL^T AGM 02 STO 01 03 X<>Y 04 STO 02 05 X<>Y 06 LBL 00 07 RCL 02 08 RCL 01 09 ENTER 10 R↑ 11 R↑ 12 X<>Y 13 R↓ 14 ENTER 15 R↑ 16 + 17 2 18 / 19 STO 01 20 R↓ 21 * 22 SQRT 23 STO 02 24 R↑ 25 - 26 ABS 27 1E-10 28 X≤Y? 29 GTO 00 30 CLA 31 ^T AGM = 32 ARCL 01 33 AVIEW 34 END HP 42S/Swiss Micros DM42/Free42 Program AGM: 00 {53-Byte Prgm} 01 LBL "AGM" 02 STO 01 03 X<>Y 04 STO 02 05 X<>Y 06 LBL 00 07 RCL 02 08 RCL 01 09 ENTER 10 R↑ 11 R↑ 12 X<>Y 13 R↓ 14 ENTER 15 R↑ 16 + 17 2 18 / 19 STO 01 20 R↓ 21 * 22 SQRT 23 STO 02 24 R↑ 25 - 26 ABS 27 1E-10 28 X≤Y? 29 GTO 00 30 CLA 31 "AGM = " 32 ARCL 01 33 AVIEW 34 END The instructions for both the HP 41C and 42S versions are same: enter X and Y on the respective stacks and XEQ AGM. Example (ALL/STD mode is applied): AGM(37, 78): 37, 78, XEQ AGM returns: Alpha: AGM = 55.5947005279 Blog Post: http://edspi31415.blogspot.com/2020/07/h...metic.html |
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Messages In This Thread |
(41C) and (42S) Arithmetic-Geometric Mean - Eddie W. Shore - 07-26-2020 07:50 PM
RE: (41C) and (42S) Arithmetic-Geometric Mean - Werner - 07-27-2020, 07:26 AM
RE: (41C) and (42S) Arithmetic-Geometric Mean - Albert Chan - 07-29-2020, 11:37 AM
RE: (41C) and (42S) Arithmetic-Geometric Mean - Werner - 07-29-2020, 12:53 PM
RE: (41C) and (42S) Arithmetic-Geometric Mean - Albert Chan - 07-29-2020, 02:35 PM
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