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242 B: More About Calculations
File name : 17BII-Plus-Manual-E-PRINT-030709 Print data : 2003/7/11
Iterative Solutions
If the Solver is not able to isolate the unknown variable, it cannot
provide a direct solution. In these cases, the Solver searches iteratively
for a solution.
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In its iterative search for a solution, the Solver looks for a value that sets
the left side of the equation equal to the right side. To do this, the Solver
starts with two initial estimates of the answer, which we’ll call estimate
#1 and estimate #2. Using estimate #1, the Solver calculates values for
the left and right side of the equation (LEFT and RIGHT) and calculates
LEFT minus RIGHT (LEFT－RIGHT). Then, the Solver does the same
calculations for estimate #2. If neither estimate produces a value of zero
for LEFT－RIGHT, the Solver analyzes the results and produces two new
estimates that it judges to be closer to the answer. By repeating this
process many times, the Solver narrows in on the answer. During this
search, the calculator displays the two current estimates and the sign of
(LEFT－RIGHT) for each estimate, as shown.
Sign of LEFT－RIGHT for each estimate
Since calculators cannot do calculations with infinite precision (the HP
17bII+ uses 12 digits in its calculations), sometimes the Solver will be
unable to find an estimate where LEFT－RIGHT is exactly zero. However,
the Solver can distinguish between situations where the current estimate
could be a solution, and situations where no solution is found.
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Exceptions: (1) Occurrences of the unknown variable as the argument of the S
function are ignored. (2) The unknown variable can appear twice within an IF
function: once in the then clause and once in the else clause.