A new high-order derivative-free method for the solution of a nonlinear equation is developed. The novelty use Traub’s as first step. order proven and demonstrated. It also shown that has much fewer divergent points runs faster than an optimal eighth-order method.

In this article, a model free adaptive control with the estimated pseudo partial derivative (PPD) is introduced by multi-input fuzzy rules emulated network (MiFREN) for a class of discrete-time systems. The resetting mechanism can be relaxed in this adaptation scheme. Human knowledge about the controlled plant is rearranged to define the IF-THEN rules directly. Those fixed parameters are design...

We consider the non-Hermitian Hamiltonian H = − d dx + P (x) − (ix) on the real line, where P (x) is a polynomial of degree at most n ≥ 1 with all nonnegative real coefficients (possibly P ≡ 0). It is proved that the eigenvalues λ must be in the sector | argλ| ≤ π 2n+3 . Also for the case H = − d dx − (ix) , we establish a zero-free region of the eigenfunction u and its derivative u and we find...

A derivative-free Quasi-Newton (DFQN) method previously published [J. Greenstadt, Math. Comp., v. 26, 1972, pp. 145—166] has been revised and simplified. The main modification has the effect of keeping all the successive approximants to the Hessian matrix positive-definite. This, coupled with some improvements in the line search, has enhanced the performance of the method considerably. The resu...