Linear Splines Given domain a,b,a spline S(x) Is defined on entire domain .Provides continuity,i.e.,is Co[a,b] partition of "knots" ta=to,ti,t2,...,tn=b} such that S(x)=ax+b∈P([t,ti+1]),i=0,,n-1 Recall:no y-values or interpolation yet Copyright©2011NA⊙Yin 8Linear Splines Given domain [a, b],a spline S(x) • Is defined on entire domain • Provides continuity,i.e.,is C 0 [a, b] • ∃ partition of ”knots” {a = t0, t1, t2, . . . , tn = b} such that Si(x) = aix + bi ∈ P1([ti , ti+1]), i = 0, . . . , n − 1 Recall:no y−values or interpolation yet Copyright c 2011 NAYin 8