Reconstruction matrices and calibration relations for minimal splines

On a nonuniform gird, we consider twice continuously differentiable splines of third order and obtain calibration relations expressing the coordinate splines on the original grid as a linear combination of splines of the same type on a refined grid. We also obtain calibration relations representing the coordinate splines on an enlarged grid as a linear combination of splines of the same type on the original grid. We derive the reconstruction matrices on an interval and on a segment for the space of third order splines associated with infinite and finite nonuniform grids respectively. Bibliography: 10 titles.