Shape preserving interpolatory subdivision schemes for nonuniform data
The article is devoted to the problem of shape preserving four-point subdivision schemes that are stationary and interpolate nonuniform univariate data \( \{ (x_i,f_i) \} \), where \( x_i \neq x_j \) if \( i \neq j \). Performed subdivision is made in a way to get the grid locally uniform. There is constructed suitable subdivision methods for the \(f\) -data preserving convexity. It is presented a sufficient condition for preservation of convexity. There is generated a continuously differentiable limit function from initial convex data. The schemes are restricted to those that reproduce quadratic polynomials. Derived schemes are third order accurate. The linear schemes are examined as well.
scientific article; zbMATH DE number 1763601
scientific article