Publisher:

Chapman & Hall/CRC

Number of Pages:

936

Price:

109.95

ISBN:

9781584889786

Date Received:

Monday, July 7, 2008

Reviewable:

No

Reviewer Email Address:

Series:

Chapman & Hall/CRC Numerical Analysis and Scientific Computing 2

Publication Date:

2008

Format:

Hardcover

Audience:

Category:

Monograph

**Preliminaries and Tutorials** **Applications of Linear Approximation**

Applications to social sciences and economics

Applications to industry

Applications to digital images**Preliminaries**

Discrete linear approximation and solution of overdetermined linear equations

Comparison between the L_{1}, the L_{2}, and the L_{∞} norms by a practical example

Error tolerances in the calculation

Representation of vectors and matrices in C

Outliers and dealing with them**Linear Programming and the Simplex Algorithm**

Notations and definitions

The simplex algorithm

The simplex tableau

The two-phase method

Duality theory in linear programming

Degeneracy in linear programming and its resolution

Linear programming and linear approximation

Stability of the solution in linear programming**Efficient Solutions of Linear Equations**

Vector and matrix norms and relevant theorems

Elementary matrices

Gauss LUdecomposition with complete pivoting

Orthogonal factorization methods

Gauss–Jordan method

Rounding errors in arithmetic operations**The L _{1} Approximation**

Linear programming formulation of the problem

Description of the algorithm

The dual simplex method

Modification to the algorithm

Occurrence of degeneracy

A significant property of the L

Triangular decomposition of the basis matrix

Arithmetic operations count

Numerical results and comments

C source code

A special problem of a general constrained one

Linear programming formulation of the problem

Description of the algorithm

Numerical results and comments

C source code

A special problem of a general constrained one

Linear programming formulation of the problem

Description of the algorithm

Numerical results and comments

C source code

Approaches to polygonal approximation

The L

Description of the algorithm

Linear programming technique

Numerical results and comments

C source code

Characteristics of the piecewise approximation

The discrete linear L

Description of the algorithms

Numerical results and comments

C source code

Linear programming formulation of the problem

Description of the algorithm

A significant property of the Chebyshev approximation

Numerical results and comments

C source code

A special problem of a general constrained one

Linear programming formulation of the problem

Description of the algorithm

Numerical results and comments

C source code

A special problem of a general constrained one

Linear programming formulation of the problem

Description of the algorithm

Numerical results and comments

C source code

A special problem of general constrained algorithms

Linear programming formulation of the problem

Description of the algorithm

The triangular decomposition method

Arithmetic operations count

Numerical results and comments

C source code

The problem as presented by Descloux

Linear programming analysis of the problem

Numerical results and comments

C source code

Characteristic properties of piecewise approximation

The discrete linear Chebyshev approximation problem

Description of the algorithms

Numerical results and comments

C source code

Pattern classification problem

Solution of the system of linear inequalities Ca > 0

Linear one-sided Chebyshev approximation algorithm

Linear one-sided L

Numerical results and comments

C source code

Least squares solution of linear equations

Factorization of matrix A

Explicit expression for the pseudo-inverse

The singular value decomposition (SVD)

Practical considerations in computing

Linear spaces and the pseudo-inverses

Multicollinearity, collinearity, or the ill-conditioning of matrix A

Principal components analysis (PCA)

Partial least squares method (PLS)

Ridge equation

Numerical results and comments

C source code

Characteristics of the approximation

The discrete linear least squares approximation problem

Description of the algorithms

Numerical results and comments

Updating and downdating techniques

C source code

Solution of ill-posed linear systems

Estimation of the free parameter

Description of the new algorithm

Optimum value of the rank

Use of linear programming techniques

Numerical results and comments

C source code

Linear programming formulation of the problem

Description of the algorithm

Numerical results and comments

C source code

Linear programming formulation of the two problems

Description of the algorithms

Numerical results and comments

C source code

The linear programming problem

Description of the algorithm

Numerical results and comments

C source code

Quadratic programming formulation of the problems

Solution of problem (E0)

Solution of problem (E)

Numerical results and comments

C source code

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