HP Prime and Casio fx-CG50 Condition Number of a Function
Introduction
Condition number for a function f(x) is:
Cond = abs( x * d/dx f(x) / f(x) )
If the condition number is low, then function is not sensitive to small changes. This is similar to the condition number for matrices, where a low number gives for a well-conditioned problem while a higher number gives for an ill-conditioned problem.
HP Prime Program CONDFX
Arguments: f(X) as a string, use the capital X as a variable; a: value
Syntax: CONDFX(f, a)
EXPORT CONDFX(f,a)
BEGIN
// f(X) as a string, x0
// 2020-02-06 EWS
X:=a;
fx:=EXPR(f);
X:=a+.0001;
dx:=(EXPR(f)-fx)/.0001;
c:=ABS(a*dx/fx);
RETURN c;
END;
Note: The derivative is calculated manually.
Example: (in Radians mode)
CONDFX("2*X*COS(X)",1.5) returns 20.15361502
CONDFX("e^-(.25*X)",1.5) returns 0.374995308312
Casio fx-CG 50 Program FCOND
"2020-02-05 EWS"
"NO QUOTES NEEDED"
Rad
"F(X): "?→Y1
"X0: "?→A
Abs( A * d/dx(Y1,A) ÷ Y1(A))→C
Note: Y1 is from the VARS, Graphic menu.
Example:
F(X): 2*X*COS(X), X0: 1.5; Result: 20.15212992
F(X): e^(-.25*X), X0: 1.5; Result: 0.375
Source:
Condition Number. Wikipedia. https://en.wikipedia.org/wiki/Condition_number Retrieved February 1, 2020
Eddie
All original content copyright, © 2011-2020. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
Introduction
Condition number for a function f(x) is:
Cond = abs( x * d/dx f(x) / f(x) )
If the condition number is low, then function is not sensitive to small changes. This is similar to the condition number for matrices, where a low number gives for a well-conditioned problem while a higher number gives for an ill-conditioned problem.
HP Prime Program CONDFX
Arguments: f(X) as a string, use the capital X as a variable; a: value
Syntax: CONDFX(f, a)
EXPORT CONDFX(f,a)
BEGIN
// f(X) as a string, x0
// 2020-02-06 EWS
X:=a;
fx:=EXPR(f);
X:=a+.0001;
dx:=(EXPR(f)-fx)/.0001;
c:=ABS(a*dx/fx);
RETURN c;
END;
Note: The derivative is calculated manually.
Example: (in Radians mode)
CONDFX("2*X*COS(X)",1.5) returns 20.15361502
CONDFX("e^-(.25*X)",1.5) returns 0.374995308312
Casio fx-CG 50 Program FCOND
"2020-02-05 EWS"
"NO QUOTES NEEDED"
Rad
"F(X): "?→Y1
"X0: "?→A
Abs( A * d/dx(Y1,A) ÷ Y1(A))→C
Note: Y1 is from the VARS, Graphic menu.
Example:
F(X): 2*X*COS(X), X0: 1.5; Result: 20.15212992
F(X): e^(-.25*X), X0: 1.5; Result: 0.375
Source:
Condition Number. Wikipedia. https://en.wikipedia.org/wiki/Condition_number Retrieved February 1, 2020
Eddie
All original content copyright, © 2011-2020. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
