Uniform-norm stability of a B-spline basis ($d_k^{-1}\Vert a{\Vert }_{{\ell }^{\infty }}\le \Vert {\sum }_i{a}_i{N}_i{\Vert }_{\infty }\le \Vert a{\Vert }_{{\ell }^{\infty }}$)

For a linearly independent partition-normalized B-spline basis, equivalence of norms gives a lower coefficient-stability constant. The upper bound follows from the subpartition of unity for B-splines. A knot-independent stability bound can be chosen depending on spline order. This norm comparison transfers matrix estimates to the B-spline interpolation operator norm.