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Numerical Algorithm for Analysis of n-ary Subdivision Schemes

The analysis for continuity of limit curves generated by m-point n-ary subdivision schemes is presented for m, n ≥ 2. The analysis is based on the study of corresponding differences and divided difference schemes. A numerical algorithm is introduced which computes the continuity and higher order divided differences of schemes in an efficient way. It is also free from polynomial factorization and division unlike the well-known Laurent polynomial algorithm for analysis of schemes which depends on polynomial algebraic operations. It only depends on the arithmetic operations.