现代数值计算方法(matlab版)第5章(1)new

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2、I=f(x)dxa3/16¥ȼêf(x),,OZbI=Ln(x)dx(5.1)aÈ©Cq,ùïá¦Èúª¡.¦Èúª.^õªLn(x)LªXnJJLn(x)=lk(x)f(xk)IIk=0J(5.1)XnII=Akf(xk),(5.2)Backk=0CloseÙ¥ZbZbYnx−xjAk=lk(x)dx=dx(5.3)aaxk−xj福建师范大学j=0数计学院j6=kZb4/16(x−x0)···(x−xk−1)(x−xk+1)···(x−xn)=dxa(xk−x0)···(xk−xk−1)(xk

3、−xk+1)···(xk−xn)¡¦ÈXê,xk(k=0,1,···,n)K¡¦È!:.5`,IÑØuI∗°(,§¡¦Èúª(5.2){,äØ.d{úª,éu.¦Èúª(5.3),Ù{JJZIIbf(n+1)(ξ)∗R[f]=I−I=ω(x)dx,(5.4)Ja(n+1)!IÙ¥ξCþxk',ω(x)=(x−x0)(x−x1)···(x−xn).BackCloseÏ~^¤¢ê°ÝL«¦ÈúªØ.e¡Ñê°Ý½Â.福建师范大学½Â5.1XJ¦Èúª(5.2)éuØLmgõª´数计学院O(,=

4、R[f]=0¶éum+1g±þõª´ØO(,K5/16¡¦Èúª(5.2)ê°Ým.

5、^ê°ÝVg,±e¡(Ø.½n5.1¦Èúª(5.2)´.¦Èúª¿^´µ§ê°Ýn.JJy75.eúª(5.2)´.¦Èúª,K(5.4)¤á.éIIugêØLnõªf(x),Ù{R[f]=0,d¦ÈúªJ(5.2)ê°Ýn.IBack¿©5.e¦Èúª(5.2)ê°Ýn,K§éuÄClose¼êlk(x)(k=0,1,···,n)´O(,=kZbXnlk(x)dx=Ajlk(xj),aj=

6、0福建师范大学数计学院dulk(xj)=δkj,þªm>¢SþÒuAk,=Z6/16bAk=lk(x)dxa¤á,(5.2)´.¦Èúª.~5.1y²e¡¦Èúªäk3gê°Ý:Z11100f(x)dx≈f(0)+f(1)−f(1)−f(0).(5.5)JJ0212IIy(1)-f(x)=1,¦Èúª(5.5),>=1=m>.J(2)-f(x)=x,¦Èúª(5.5),ZI11111>=xdx==m>=(0+1)−(1−1)=,Back022122Close(3)-f(x)=x2,¦Èúª(

7、5.5),Z11111112>=xdx==m>=(0+1)−(2−0)=−=.32122630福建师范大学数计学院(4)-f(x)=x3,¦Èúª(5.5),Z17/161111113>=xdx==m>=(0+1)−(3−0)=−=.042122444)-f(x)=x4,¦Èúª(5.5),Z11111114>=xdx=6=m>=(0+1)−(4−0)=−=.05212236þãL²,¦Èúª(5.5)éØL3gõª´O(,é3gJJ±þõª´ØO(.âê°Ý½Â,¦Èúª(5.5)äkII3gê°

8、Ý.JIe¡·5?ئÈXêAkO.B,·å!Back:,=rÈ©«m[a,b]¿©¤n©.-Úh=(b−a)/n,¿PClosex0=a,xn=b,Kn+1!:xk=x0+kh,k=0,1,···,n.福建师范大学C数计学院x−x0t=,8/16h¦ÈXêúª(5.3)Zb(x−x0)···(x−xk−1)(x−xk+1)···(x−xn)Ak=dxa(xk−x0)···(xk−xk−1)(xk−xk+1)···(xk−xn)Znhnt(t−1)···(t−k+1)(t−k−1)···(t−n)=hdt

9、(5.6)0(−1)n−khn(n−k)!k!JJZ(−1)n−khnII=t(t−1)···(t−k+1)(t−k−1)···(t−n)dt.(n−k)!k!0JIù«å!:.¦ÈúªÏ~¡Úî-Adúª.e¡0BackAÚî-AdúªAÏ/ª¿©ÛÙäØ.Close§5.2A~^¦Èúª§5.2.1F/úª9ÙØ福