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

where an ≠ 0. The function imsl_f_zeros_poly finds zeros of a polynomial with real coefficients using the Jenkins-Traub method.

The function imsl_f_zeros_function finds the real zeros of a real, continuous, univariate function. It uses a meta-algorithm based on partitioning the interval using a low-discrepancy sequence and a combination of Müller’s method and Brent’s method. This algorithm can find roots without requiring the user to bracket the root in an interval over which the function changes sign, as required by Brent’s method, or give good guesses for the roots, as required by Müller’s method.

The function imsl_f_zero_univariate finds a real zero of a real, continuous, univariate function. It uses an algorithm attributed to Dr. Fred T. Krogh, JPL, 1972. Tests have shown this algorithm to require fewer function evaluations, on average, than a number of other algorithms for finding a zero of a continuous function.

A system of equations can be stated as follows:

where x ∈ ℜn, and fi : ℜn → ℜ.The function imsl_f_zeros_sys_eqn uses a modified hybrid method due to M.J.D. Powell to find the zero of a system of nonlinear equations.