Splines Given domain [a,b],a spline S(x) Is defined on entire domain Provides a certain amount of smoothness 3partition of"knots"(=where spline can change form) {a to,t1,t2;...:tn=bh such that So(x),x∈[to,t], S(x)= S(x),x∈[t1,t2], Sn-1(x),x∈[tn-1,tn] is piecewise polynomial Copyright 2011 NAOYin 5 Splines Given domain [a, b],a spline S(x) • Is defined on entire domain • Provides a certain amount of smoothness • ∃ partition of ”knots”(=where spline can change form) {a = t0, t1, t2, . . . , tn = b} such that S(x) =    S0(x), x ∈ [t0, t1], S1(x), x ∈ [t1, t2], ... Sn−1(x), x ∈ [tn−1, tn] is piecewise polynomial Copyright c 2011 NAYin 5