數(shù)值分析課后題答案

1、數(shù)值分析數(shù)值分析第二章2當(dāng)當(dāng)時，時，求的二次插值多項式。的二次插值多項式。112x??()034fx??()fx解：012012120010202110120122021112()0()3()4()()1()(1)(2)()()2()()1()(1)(2)()()6()()1()(1)(1)()()3xxxfxfxfxxxxxlxxxxxxxxxxxlxxxxxxxxxxxlxxxxxxx????????????????????????

2、?????????則二次拉格朗日插值多項式為220()()kkkLxylx???0223()4()14(1)(2)(1)(1)23537623lxlxxxxxxx?????????????6設(shè)設(shè)為互異節(jié)點，求證：為互異節(jié)點，求證：01jxjn??（1）0()nkkjjjxlxx???(01)kn??（2）0()()0nkjjjxxlx????(01)kn??證明（1）令()kfxx?若插值節(jié)點為，則函數(shù)的次插值多項式為。01jxjn??

3、()fxn0()()nknjjjLxxlx???插值余項為(1)1()()()()()(1)!nnnnfRxfxLxxn????????又kn????012012102()()1()()21()41()4xxxxxxxxxxba?????????????????又?21max()()max().8axbaxbfxbafx????????8在在上給出上給出的等距節(jié)點函數(shù)表，若用二次插值求的等距節(jié)點函數(shù)表，若用二次插值求的近似值，要使的近似

4、值，要使44x???()xfxe?xe截斷誤差不超過截斷誤差不超過，問使用函數(shù)表的步長，問使用函數(shù)表的步長h應(yīng)取多少？應(yīng)取多少？610?解：若插值節(jié)點為和，則分段二次插值多項式的插值余項為1iixx?1ix?2111()()()()()3!iiiRxfxxxxxx??????????211441()()()()max()6iiixRxxxxxxxfx?????????????設(shè)步長為h，即11iiiixxhxxh??????434321