Reduction in the Case of Equal Intervals

Here the yj s are (A — 1) unknowns, which are obtainable by imposing the - 1 conditions that S (icj) = j / (/ = 1, 2. .. Af — 1) and then resolving a linear system of equations. The above reduction is of importance because of the high stability and simplicity of the cardinal splines on a mesh of regularly spaced abscissas. 

The structure of this formula is interesting. The X s and fi s lying by definition between 0 and 1, is a band matrix with a dominant diagonal = 2). The same is approximately true for close to 0.5). This shows that the m, s are re- 

---