A priori determination of breakpoints z∈x.X (2 f(=)=L(=)+ f2(n) 2(z-x,)x-x1) Mh2 f(=)-L(z)k z∈[a,B f(=)-L(z)≤ M2h M2( B-a 8 8 n21+(B-a)M,/88Static
A priori determination of breakpoints [ , ] i i+1 z x x ( )( ) 2 ( ) ( ) ( ) 1 (2) = + − i − i+ z x z x f f z L z 8 | ( ) ( )| 2 M2 h f z − L z z [, ] − − − = 2 2 2 2 8 8 1 | ( ) ( )| n M h M f z L z n 1+( −) M2 /8 Static
Adaptive Piecewise Linear Interpolation roblem I Interpolation of humps()with pwL, n=5
Adaptive Piecewise Linear Interpolation Problem
Adaptive Piecewise Linear Interpolation acceptable xL,xR xL+xr f(xL)+f(R) < 2 or xR-xlsh mIn
Adaptive Piecewise Linear Interpolation acceptable [xL, xR] + − + 2 ( ) ( ) 2 x L x R f x L f x R f hmin or xR− xL
delta= 1. 0000 Static n= 151 delta= 1 0000 Adapt n= 21 40
delta= 1. 0000 Static n= 151 delta= 1 0000 Adapt n= 21 100 E