On identification of a wave number for Helmholtz equation

This note is concerned with inverse evaluation of an unknown wave number in a Helmholtz equation. The algorithm assumes an initial guess for the unknown function and obtains corrections to the guessed value. The updating stage is accomplished by generating a set of functions that satisfy some of the required boundary conditions. We refer to this space as proper solution space. The correction to the assumed value can then be obtain by imposing the remaining boundary conditions. We consider the evaluation of real and complex wave numbers. A number of numerical examples are used to study the applicability and effectiveness of the procedure.