中图苔技术大荸数学系 University of Science and Technology of China DEPARTMENT OF MATHEMATICS 求{l(x)}o,易知: l1(x)=a1(x-x0)…(x-x1-1)(x-x1+1)……(x-xn) )…(x )(x i+1 ●线性插值 X-X X-x 70(x)= (x) X1 L(x)=f(x0)(x)+f(x1)4(x)数 学 系 University of Science and Technology of China DEPARTMENT OF MATHEMATICS ⚫线性插值 1 0 0 1 0 1 1 0 ( ) , ( ) x x x x l x x x x x l x − − = − − = ( ) ( ) ( ) ( ) ( ) 1 0 0 1 1 L x = f x l x + f x l x 求 n i x i l 0 { ( )} = ，易知： ( ) ( ) ( )( ) ( ) i x ai x x0 x xi 1 x xi 1 x xn l = −  − − − +  − ( ) ( )( ) ( ) 1 i 0 i i 1 i i 1 i n i x x x x x x x x a − − − − =  − + 