Name

loop — Maximum Width Property applied on given Polynomial function.

Description

Application of Maximum Width Rule. Used for subdiving the box in the longest edge direction at the midpoint. This process generates two subdivided boxes.

These subdivided boxes undergo Vertex Property, and Cutoff Test.

Examples

// Maximum Width Property applied on given Polynomial function
// Whichever box having maximum differece between lower and upper bounds, taken for subdivision process.
// Like in this example say,
X= [0,1;-1,2], //second row taken for process.

   

See also

InvUVW, vertex, cutoff

Authors

Mr. Dhiraj B. Magare
IDP in Systems and Control Engineering
Indian Institute of Technology Bombay
Mr. Bhagyesh V. Patil
IDP in Systems and Control Engineering
Indian Institute of Technology Bombay
Prof. P.S.V. Nataraj
IDP in Systems and Control Engineering
Indian Institute of Technology Bombay

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. G. T. Cargo and O. Shisha. The Bernstein form of a polynomial. Jl. of research of NBS,70B:79-81,1966.

3. 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.