Monday, November 19, 2012

Polynomial intervals, not interval polynomials!

Following Walid's suggestion, Jan implemented splitting of initial condition boxes during IVP solving as a way to obtain narrowing enclosures for stable ODEs, such as x' = -x and x'' = -x'-x. Jan noticed that the current representation of solutions for IVPs as linear interval polynomials does allow for representation of narrowing enclosures. This forces the enclosures to widen between segments and prevents the piece-wise solution from converging. The way to allow narrowing enclosures while retaining a piece-wise affine representation of enclosures is to use pairs of linear interval polynomials to bound the solution.