Overview: Nonlinear Equations

This section introduces some of the mathematical concepts used with IDL Advanced Math and Stats.

Zeros of a Polynomial

A polynomial function of degree n can be expressed as follows:

p(z) = a_nzⁿ + a_n–1z^{n – 1} + ... + a₁z + a₀

where a_n ≠ 0. The IMSL_ZEROPOLY function finds zeros of a polynomial with real or complex coefficients using either the companion method or the Jenkins-Traub three-stage algorithm.

Zeros of a Function

The IMSL_ZEROFCN function uses Müller's method to find the real zeros of a real-valued function.

Root of System of Equations

A system of equations can be stated as follows:

f_i(x) = 0, for i = 0, 1, ..., n – 1

where , and f_i : Rⁿ → R.

The IMSL_ZEROSYS function uses a modified hybrid method due to M.J.D. Powell to find the zero of a system of nonlinear equations.