Interpolatory Linear Splines ●Given points {(to,y0),(t1,y1),(t2,y2,,(tn,yn)} spline must interpolate as well .Are the Si(z)(with no additional knots)unique? Coefficients:aix+bi,i=0,...,n-1 =total=2n Conditions:2 prescribed interpolation points for Si(),i=0,...,n-1(includes continuity condition)=total=2n ●Obtain S(）=ax+(5-at,a=班+1-，i=0,.,n-1 titi-ti Copyright©2011NA⊙Yin 10Interpolatory Linear Splines • Given points {(t0, y0),(t1, y1),(t2, y2), . . . ,(tn, yn)} spline must interpolate as well • Are the Si(x)(with no additional knots)unique? ∗ Coefficients:aix + bi , i = 0, . . . , n − 1 ⇒total= 2n ∗ Conditions:2 prescribed interpolation points for Si(x), i = 0, . . . , n − 1(includes continuity condition)⇒total= 2n • Obtain Si(x) = aix + (yi − aiti), ai = yi+1 − yi ti+1 − ti , i = 0, . . . , n − 1 Copyright c 2011 NAYin 10