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This book takes in some of the latest mathematical applications derived from Newtonian law. It explains the mechanical method for determining matrix singularity or non-independence of dimension and complexity, and includes new approaches to standard problems.

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Newtonian Nonlinear Dynamics for Complex Linear and Optimization Problems explores how Newton´s equation for the motion of one particle in classical mechanics combined with finite difference methods allows creation of a mechanical scenario to solve basic problems in linear algebra and programming. The authors present a novel, unified numerical and mechanical approach and an important analysis method of optimization.

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Elements of Newtonian Mechanics.- Solution of Systems of Linear Equations.- Linear Systems: Numerical Simulations.- Eigenvalue Problems.- Eigenvalue Problems: Numerical Simulations.- Linear Programming.- Quadratic Programming.

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From the reviews:
"The framework of the monograph is the construction of algorithms for linear and nonlinear optimization problems by applying numerical algorithms used to simulate the equation of motion for Newtonian particles. ... The monograph is intended for a broad public, for undergraduate and graduate students and for researchers. ... There are illustrative examples in two or three variables at the end of each chapter. Several figures help the reader to understand the methods." (Werner H. Schmidt, Zentralblatt MATH, Vol. 1264, 2013)

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Luis Vazquez, Universidad Complutense de Madrid, lvazquez@fdi.ucm.es
Salvador Jimenez, Universidad Politecnica de Madrid, s.jimenez@upm.es

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