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Chapter 2
Some Fundamental
Numerical Methods
It is necessary to create several computing aids before addressing specific
design tasks. Certainly the most elementary of these is a hand-held computer
program to calculate the complex four functions. Also, the solution of linear
systems of equations, both in real and complex variables, and numerical
integration are useful in many electrical engineering applications. The former
is required in the last part of this chapter to fit discrete, complex data by
a rational polynomial in the frequency variable to the least-squared-error
criterion. Before that, a piecewise linear function will be approximated in the
minimum-of-maximum-errors (minimax) sense by a polynomial in a real
variable. This is a useful tool that allows the introduction of the versatile
Chebyshev polynomials, which will make several later appearances.
2.1. Complex Four Functions
The convenience of addition, subtraction, multiplication, and division of
complex numbers on a hand-held calculator, both manually and within
programs, cannot be overrated. Program A2-1 in Appendix A provides these
subroutines on function keys B, C, and D for manual keying or for GSB (Go
Subroutine) commands within programs. As explained in the program description,
the more frequently required polar complex number format has been
assumed.
Hopefully, the reverse Polish (RPN) stack concept is somewhat familiar to
the reader, since it has been used by many calculator manufacturers in several
countries. Owners of calculators with the algebraic operating system (AOS)
are at no great disadvantage, because RPN programs are easily converted (see
Murdock, 1979). In Program A2-1 and in similar programs to follow, the polar
complex number(s) are entered into the calculator's XYZT "stack" as angle in
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