摘要：當(dāng)節(jié)點(diǎn)較多時(shí)多項(xiàng)式插值很不穩(wěn)定,而有理插值很多時(shí)候能克服這個(gè)弱點(diǎn),但是有理插值有時(shí)候會(huì)出現(xiàn)極點(diǎn).介紹一種與節(jié)點(diǎn)分布無關(guān)且無極點(diǎn)的高階有理插值,對(duì)于光滑性較好的函數(shù),高階有理插值逼近誤差為O(h^d+1),對(duì)于不光滑的函數(shù)逼近誤差近似為O(h).在實(shí)際應(yīng)用中高階有理插值有很好的效果.