Well, I'm going to give it a try.
I assume that your expression "But I really can not let LabVIEW loop to work this out" does not mean that you can NOT use loops
🙂First, in your expression y=f(x), if you know the value of "y", you can always equate the expression to zero:
f(x) - y = 0
The problem is now to find the roots of the equation. If that's allowed, then you may want to try LabVIEW's mathematical VIs, which are located in the diagram function palette -> Mathematics -> Zeroes.
If you must, need or want to use a loop, for example a While loop, you may want to use Shift Registers. Shift registers allows you to remember iteration values. To add a shift register, right-click on one of the side borders of the loop and select "Add Shift Register" from the pop
-up menu. When you do that, two registers will appear at both sides of the loop diagram. To initialize the value of a shift register, wire the left side shift register from outside.
When the loop executes, it takes the initial value (left shift register) and you can process it inside the loop using your recursive formula. When functions inside the loop ends executing, the resulting value should be the input of the right shift register. If the loop execute again, the value entered at the right side will go to the left side, so it is the new value for the next iteration. And so on.
For the condition to stop the while loop, if the solution is not going to be exact, you should define and test an error tolerance between iterations.
To extract the resulting value after the loop finish executing, wire the right shift register.
Hope this can be of help.
Regards;
Enrique Vargas
www.vartortech.com