Chapter 7: Nonlinear Equations

Usage Notes

Zeros of a Polynomial

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

p(z) = anzn + an-1 zn-1 + … + a1z + a0

where an ¹ 0. The function imsl_f_zeros_poly finds zeros of a polynomial with real coefficients using the Jenkins-Traub method.

Zeros of a Function                             

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.

Root of System of Equations

A system of equations can be stated as follows:

fi(x) = 0,  for  i = 1, 2, …, n

where x Î 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.


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