Note that I use variable names of the form yy1 to avoid contention with the built-in function variables y1
and y2. If xx1 = 1, yy1 = 1, xx2 = 2 and yy2 = 4, either of these routines returns y = 2.5 for x = 1.5.
Either of these methods are fast and work well. However, you have to remember the order of the input
variables. One way to avoid this is to use the Numeric Solver. This program automates the process:
linterp()
Prgm
©Linear interpolation with numeric solver
©Delete equation variables
delvar x,y,xx1,xx2,yy1,yy2
©Save interpolation equation
y=((yy1-yy2)*x+xx1*yy2-xx2*yy1)/(xx1-xx2)→eqn
©Start the numeric solver
setMode("Split 1 App","Numeric Solver")
EndPrgm
This program works by saving the interpolation equation to the system variable eqn, which is used by
the numeric solver. All the equation variables are deleted first, otherwise any current values will be
substituted into the equation and it will be simplified, which won't give the correct equation to solve.
Finally, the numeric solver is started with the last program line.
To use this program, enter linterp() at the command line, then press ENTER at the solver eqn: prompt.
The prompts for the six variables are shown. Enter the required values for x, xx1, xx2, yy1 and yy2,
then solve for y.
Another advantage of this program is that it is easy to find x, given y. This process is sometimes called
inverse interpolation. You can also use the interp() functions above for inverse interpolation: just enter
the y-values as x-values, then solve for y as usual, which will actually be the interpolated value for x.
[6.23] Step-by-step programs
These sites have programs that solve various problems step-by-step, that is, the program shows each
of the steps used to solve a problem. I have not tried these programs.
Oliver Miclo's ti-cas site: http://www.ti-cas.org/
! Compute derivative: stepder.89g (TI-89) or stepder.9XG (TI-92+)
! Solution of linear systems: invm()
TIcalc site: http://www.ticalc.org/pub/89/basic/math/
! Solve Diophant equations: diophant.zip
! Apply the Euclid algorithm to two numbers: euclide2.zip
! Solve a 3x3 augmented matrix with Gauss-Jordan elimination: matsol.zip
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