Description:
Didier Besset's Object-Oriented Implementation of Numerical Methods offers a wide-ranging set of objects for common numerical algorithms. Written for the math-literate Java and Smalltalk programmer, this volume demonstrates that both languages can be used to tackle common numerical calculations with ease. This title bridges the gap between pure algorithms and object design. By tackling issues like class design, interfaces, and overcoming floating-point rounding errors in both Java and Smalltalk, the code can be used as-is or as a model for your own custom numerical classes. The range of recipes, or sample numerical classes, all coded in both OOPLs, is rich. For anyone who's taken a few undergraduate math courses (like calculus, linear algebra, or statistics), plenty of the material will be familiar. After presenting some basic algorithm and mathematical principles, the book shows you the code that gets the job done (first in Smalltalk and then in Java). There's no room for demo code that shows how to use all this. The emphasis is on a good cross-section of common numerical calculations. The tour begins with calculus and moves through linear algebra, with plenty of material on matrices. Later sections on statistics cover familiar terms and calculations such as linear regression and calculations useful for establishing correlations between one or more independent variables. Sections on data mining examine the mathematical rules for finding patterns in large amounts of data. (There's also a nifty set of classes for implementing genetic algorithms.) Throughout, you get advice on choosing the right algorithm for the job. (There are class diagrams that map out how this class library is organized.) Of course, it will help to know some of the underlying math to get the most out of this intelligent and wide-ranging book, but the writing is remarkably clear and the source code is a model of intelligibility, so even readers who are averse to equations will find Object-Oriented Implementation of Numerical Methods readable. In general, any competent Java or Smalltalk programmer will be able to tap into solid mathematical code by reading it, without having to reinvent the proverbial wheel. --Richard Dragan Topics covered: - Introduction to numerical methods and objects in Java and Smalltalk
- Numerical precision and rounding errors
- Comparing floating-point numbers
- Functions in Smalltalk and Java
- Evaluating polynomials
- The error, gamma, and beta functions
- Interpolation algorithms (Lagrange, Newton, Neville, Burlirsch-Stoer, and cubic spline interpolations)
- Choosing the right interpolation method
- Iterative algorithms
- Finding the zeroes of functions (the bisection method, Newton's method, roots of polynomials)
- Integration of functions (trapeze integration method and Simpson and Romberg integration algorithms)
- Open integrals
- Choosing the right integration method
- Infinite series
- Continued fractions
- Incomplete gamma and beta functions
- Algorithms for linear algebra
- Vectors and matrices
- Linear equations (backward substitution, Gaussian elimination, LUP decomposition)
- Matrix determinants and inversion
- Eigenvalues and eigenvectors of nonsymmetrical and symmetrical matrices
- Statistical moments
- Histograms
- Probability distributions (normal, gamma, and experimental distributions)
- The F-test
- The t-test
- The chi-squared test
- Least-fit square algorithms
- Optimization algorithms
- Extended Newton algorithms
- Hill-climbing algorithms
- Powell's algorithm
- Simplex algorithm
- The genetic algorithm
- Data mining
- Covariance
- Multidimensional probability distribution
- The Mahalanobis Distance
- Cluster analysis and variance
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