Starting with a shape-preserving C-1 quadratic spline, we show how kno
ts can be removed to produce a new spline which is within a specified
tolerance of the original one, and which has the same shape properties
. We give specific algorithms and some numerical examples, and also sh
ow how the method can be used to compute approximate best free-knot sp
lines. Finally, we discuss how to handle noisy data, and develop an an
alogous knot removal algorithm for a monotonicity preserving surface m
ethod.