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Researchers are faced with the problem of solving a variety of equations in the course of their work in engineering, economics, physics, and the computational sciences. This book focuses on a new and improved local-semilocal and monotone convergence analysis of efficient numerical methods for computing approximate solutions of such equations, under weaker hypotheses than in other works. This particular feature is the main strength of the book when compared with others already in the literature.The explanations and applications in the book are detailed enough to capture the interest of curious readers and complete enough to provide the necessary background material to go further into the subject.
A text surveying perturbation techniques and sensitivity analysis of linear systems is an ambitious undertaking, considering the lack of basic comprehensive texts on the subject. A wide-ranging and global coverage of the topic is as yet missing, despite the existence of numerous monographs dealing with specific topics but generally of use to only a narrow category of people. In fact, most works approach this subject from the numerical analysis point of view. Indeed, researchers in this field have been most concerned with this topic, although engineers and scholars in all fields may find it equally interesting. One can state, without great exaggeration, that a great deal of engineering work is devoted to testing systems' sensitivity to changes in design parameters. As a rule, high-sensitivity elements are those which should be designed with utmost care. On the other hand, as the mathematical modelling serving for the design process is usually idealized and often inaccurately formulated, some unforeseen alterations may cause the system to behave in a slightly different manner. Sensitivity analysis can help the engineer innovate ways to minimize such system discrepancy, since it starts from the assumption of such a discrepancy between the ideal and the actual system.