|Re: Equation problem in Hp32II (summing it up)|
Message #15 Posted by Karl Schneider on 7 Jan 2006, 1:22 a.m.,
in response to message #14 by Ravinder Walia
A few good points by several people in this thread. I'll try to sum it all up.
To recap, the problem was to solve the equation
D = 10 * LOG(W/0.001)
for D = 12.0 on an HP-32SII in Equation mode.
Indeed, the HP-32SII solves only iteratively, unlike the HP-33S, which will return an algebraically-derived direct solution if it deems possible.
The 32SII will use the stored value of the variable to be solved, and the value in the x-register as the first guesses for the solution. This is true when solving an equation or a program.
In equation mode, when the user enters 12 as the prompted value of D, that unfortunately is one of the guesses for the solution of W. Pre-storing a positive value for W that is less than, or close enough to the solution W = 0.001*(10^1.2) = 0.015849 will ensure that the algorithm will converge. A larger pre-stored value will cause the algorithm to project the next guess for W from the first two guesses into the undefined non-positive region, causing an error.
Pre-storing a positive value of W that is less than the actual solution will bound it between 12, bringing convergence. Pre-storing W = 0.02 will also work. However, Pre-storing W = 0.1 will fail, as the next projection of W -- based on function values calculated at W = 0.1 and W = 12.0 -- is negative.
One way to get around this problem is to enter the equation as a program, so that two legitimate guesses can be entered.
The methods of the HP-33S are more adroit: It will solve the equation directly.