B样条基扩充节点的选择

样条在［ａ，ｂ］区间的Ｂ样条表示需要在区间（ａ，ｂ）外引进附加的节点．本文证明了，若选择所有的附加节点分别为端点ａ和ｂ，那么矩阵（Ｎｊ，ｋ）的范数可以达到最小．同时这样的选择可以简化算法．特别，人们可以用高斯主元消去法稳定地计算Ｂ样条系数，即使对应的矩阵并不全正，也不是对角优势的情况也是如此．

On the Choice of the Exterior Knots in the B-spline Basis

The B-spline representation of a spline on some intervala,b] requires the introduction of additional knots outage (a,b) that have nothing in common with the spline space itself. In this note, it is shown that locating all these additional knots at the endpoints a and b of the interval minimises the matrix matrix norm of the matrix where aregiven linear interpolation conditions, and so is preferable when the B-spline representation of a spline interpolant is to be constructed. Such a choice usually also simpofies the algorithms. In particular, one is able to compute stubly the B-spline coeffiCients of a complete spline interpolant by Gauss elimination without pivoting through the corresponding matrix falls to be totally positive or diagonally dominant.