The most hazardous class of pharmaceuticals for soil and aquatic ecosystems are antibiotics, which include prescription medications and cancer treatments. Hospital effluents are usually produced by all parts of medical facilities, including hospitals. This study's specific goal was to provide a quick, affordable, and accurate analytical technique for determining the levels of amoxicillin, azithromycin, and penicillin in wastewater from Medical City, Al-Mahmudiya, and Al-Yarmouk hospitals (Iraq, Baghdad). An HPLC with a receptive ODS C18 column was used. It was equipped with UV and pulsed amperometric detectors with wavelengths of 230 nm and 210-240 nm, respectively. The correlation coefficients for each drug are greater than 0.9999,

The study presents the modification of the Broyden-Flecher-Goldfarb-Shanno (BFGS) update (H-Version) based on the determinant property of inverse of Hessian matrix (second derivative of the objective function), via updating of the vector s ( the difference between the next solution and the current solution), such that the determinant of the next inverse of Hessian matrix is equal to the determinant of the current inverse of Hessian matrix at every iteration. Moreover, the sequence of inverse of Hessian matrix generated by the method would never  approach a near-singular matrix, such that the program would never break before the minimum value of the objective function is obtained. Moreover, the new modification of BFGS update (H-vers