Usage Notes¶
Zeros of a Polynomial¶
A polynomial function of degree n can be expressed as follows:
where \(a_n\neq 0\). The function zerosPoly finds zeros of a
polynomial with real coefficients using the Jenkins-Traub method.
Zeros of a Function¶
The function zerosFunction 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 zeroUnivariate 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.
Root of System of Equations¶
A system of equations can be stated as follows:
where \(x\in\Re _n\), and \(f_i : \Re_n\rightarrow\Re\). The function zerosSysEqn uses a modified hybrid method due to M.J.D. Powell to find the zero of a system of nonlinear equations.