Palindromic Matrices of Order Two and Three-Point Subdivision Schemes

We introduce a family of three-point subdivision schemes related to palindromic pairs of matrices of order 2. We apply the Mößner theorem on palindromic matrices to the C ⁰ convergence of these subdivision schemes. We study the Hölder regularity of their limit functions. The Hölder exponent which is found in the regular case is sharp for most limit functions. In the singular case, the modulus of continuity of the limit functions is of order δlogδ. These results can be used for studying the C ¹ convergence of the Merrien family of Hermite subdivision schemes.