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Global_Optimization_toolbox >> Global_Optimization_toolbox > InvUVW

InvUVW

Calculation for M

Calling Sequence

[M,N,B] = InvUVW(A,XB)

Parameters

A :

Coefficient Matrix (multidimensional matrix in case of multivariate polynomial)

XB :

Original Bounds

M :

Multiplication of Inverse of U,V and W matrix

N :

Dimension (Row) Matrix for all varibles in the Polynomial

B :

Bernstein Coefficient of the Polynomial Over given bounds XB

Description

Matrix method is used to calculate M, N and B.

Examples

// Calculation for M
[M,N,B] = InvUVW(A,XB)
// If, A=[1,2;1,0] and XB=[0.5,1];
// Gives ,
M(:).entries=[1,0.5;1,1], N=1, B=[1.5,2;2,2]

Authors

Bibliography

1. Shashwati Ray, P.S.V. Nataraj. An efficient algorithm for range computation of polynomials using the Bernstein form. Journal of Global Optimization, 45: 403-426,2009;

2. S. Ray, A new approach to range computation of polynomial problems using the Bernstein form. PhD thesis, Systems and Control Engineering, IIT Bombay, India, 2007.


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