Texas Instruments TI-89 Tip List page 263

© yy1 f1(x1)
© yy2 the mean of yy1 and yy3
© yy3 f2(x3)
© hy y-interval half-width
©
expr("define f1(x)="&f1)
expr("define f2(x)="&f2)
x2-h→x1
x2+h→x3
f1(x1)→yy1
f2(x3)→yy3
(yy1+yy3)/2→yy2
math\spli4x(yy2,x2,h,c)→x2
abs(yy2-yy1)→hy
hy/((f1(x),x)|x=x1)→xp1
hy/((f2(x),x)|x=x3)→xp3
augment(math\splice4(x1,x2,x3,xp1,xp3),{yy2,hy})
EndFunc
Note that the output list includes y2 and hy in addition to the coefficient list, since you will need them to
evaluate the inverse polynomial. If you have saved the output list in list1, then use
left(list1,5)
to extract just the polynomial coefficients, and
list[6]
to get y2, and
list[7]
to get hy.
User interface program for splice4()
The user interface program shown below, spli4ui(), automates the process of calculating a splice and
checking the results. spli4ui() finds the splice coefficients and saves them. It also calculates and
displays the errors for s(x) and the first derivatives.
spli4ui() uses a symbolic variable ä. If you have a variable ä in the current folder, it will be deleted.
spli4ui() assumes that the derivatives of the functions to be spliced can be found with the built-in
derivative function. For functions which cannot be differentiated by the calculator, you can still calculate
a splice, but you cannot use spli4ui(). See tip [6.26], Accurate numerical derivatives with nDeriv() and
Ridder's method, to find the necessary derivatives.
spl4ui()
Prgm
©splice4() user interface
©16apr02/dburkett@infinet.com
© Define local functions to be spliced
© Find splice interval bounds
© Find si(x1), si(x3)
© Find splice interval midpoint
© Solve for x at interval midpoint
© Find y-axis half-width
© Find dx/dy at x1 and x2
© Solve for splice coefficients
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