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A number of practical issues arising from tomography, image processing, etc. require the development of some nonstandard special-purpose numerical methods and software for solving large systems of linear and nonlinear equations. Issues related to the study of global properties of iterative algorithms of numerical analysis are developed. The material of this book will contribute to the doctoral enrollment, defense and more rapid scientific advancement of doctoral students and young scientists in fundamental areas of science. It will attract young scientists to master methods for numerically solving nonlinear equations, systems of linear and nonlinear equations for the study of differential equations to continue the extensive fundamental research in these modern branches of scientific knowledge. Enhanced research in mathematics, informatics and education and the obtained new methods and algorithms suggest their future implementation in new software environments through the use of distributed applications and simulations. This work is a contribution to enhancing the scientific capacity of many young scientists and researchers in the field of applicable numerical analysis.