HP Prime and Casio fx-CG50 Condition Number of a Function

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

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