Numerical methods and optimization techniques books
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BISECTION METHOD- Optimization Techniques-LECTURE 1-Numerical engg & Optimization methods
Numerical analysis is the study of algorithms that use numerical approximation as opposed to symbolic manipulations for the problems of mathematical analysis as distinguished from discrete mathematics. The growth in computing power has revolutionized the use of realistic mathematical models in science and engineering, and subtle numerical analysis is required to implement these detailed models of the world. For example, ordinary differential equations appear in celestial mechanics predicting the motions of planets, stars and galaxies ; numerical linear algebra is important for data analysis; stochastic differential equations and Markov chains are essential in simulating living cells for medicine and biology. Before the advent of modern computers, numerical methods often depended on hand interpolation formulas applied to data from large printed tables. Since the mid 20th century, computers calculate the required functions instead, but many of the same formulas nevertheless continue to be used as part of the software algorithms. The numerical point of view goes back to the earliest mathematical writings. A tablet from the Yale Babylonian Collection YBC , gives a sexagesimal numerical approximation of the square root of 2 , the length of the diagonal in a unit square.
In particular, several chapters explain optimization heuristics and how to use them for portfolio selection and in calibration of estimation and option pricing models. Such practical examples allow readers to learn the steps for solving specific problems and apply these steps to others. At the same time, the applications are relevant enough to make the book a useful reference. Matlab and R sample code is provided in the text and can be downloaded from the book's website. Stay ahead with the world's most comprehensive technology and business learning platform. With Safari, you learn the way you learn best.
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