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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.
This book also:
Presents mechanical method for determining matrix singularity or non-independence of dimension and complexity
Illustrates novel mathematical applications of classical Newton s law
Offers a new approach and insight to basic, standard problems
Includes numerous examples and applications
Newtonian Nonlinear Dynamics for Complex Linear and Optimization Problems is an ideal book for undergraduate and graduate students as well as researchers interested in linear problems and optimization, and nonlinear dynamics.
List of contents
Elements of Newtonian Mechanics.- Solution of Systems of Linear Equations.- Linear Systems: Numerical Simulations.- Eigenvalue Problems.- Eigenvalue Problems: Numerical Simulations.- Linear Programming.- Quadratic Programming.
About the author
Luis Vazquez, Universidad Complutense de Madrid, lvazquez@fdi.ucm.es
Salvador Jimenez, Universidad Politecnica de Madrid, s.jimenez@upm.es
Summary
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.
Additional text
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)
Report
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)
