现代数值计算方法(matlab版)第3章(1)new

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1、福建师范大学yêO{数计学院1/15JJII1nÙ)5§

2、{JIBackClose1nÙ)5§

3、{福建师范大学数计学院ÙïÄn5§

4、){2/15a11x1+a12x2+···+a1nxn=b1,a21x1+a22x2+···+a2nxn=b2,(3.1)············an1x1+an2x2+···+annxn=bn.e^ÝÚþPÒ5L«,(3.1)¤JJIIAx=b.(3.2)JIÙ¥,nÝA=(aij)n×n¡§

5、XêÝ,nþb=Back(b,b,···,b)T¡m

6、à,x=(x,x,···,x)T¤¦).¤¢12n12nClose{,´²LkÚ$U¦§

7、°(){.eAÛÉ,§

8、(3.1)k).e¡0A«'¢^{.福建师范大学数计学院§3.1^SGauss{9Ù§S¢y3/15Gauss{Äg´µÄk¦^Ð1Cò§

9、=zÓ)þn/§

10、(¡),2ÏL£{¦)Tn/§

11、(¡£).U1k?1Gauss{¤^SGauss{.~3.1^^SGauss{)5§

12、JJx1+x2+x3+x4=10,II−x1+2x2−3x3+x4=−2,J

13、3x1−3x2+6x3−2x4=7,IBack−4x1+5x2+2x3−3x4=0.Close)1.L§µ111110111110r2+r1−12−31−2r3−3r103−2−28r3+2r2福建师范大学−−−−→r4+4r1−−−−→r4−3r2数计学院3−36−270−63−5−234/15−452−3009614011111011111003−2−28r4+12r303−2−28−−−−→.00−1−1−70

14、0−1−1−7JJ0012−516000−17−68IIJ2.£L§µIBackClosex1+x2+x3+x4=10,x4=4,3x−2x+2x=8,x=7−x=3,福建师范大学23434⇒数计学院−x3−x4=−7,x2=(8+2x3−2x4)/3=2,5/15−17x4=−68x1=10−x1−x2−x3=1.éu5§

15、,¦^^SGauss{¦)a(1)x+a(1)x+···+a(1)x=b(1),1111221nn1(1)(1)(1)(1)a

16、21x1+a22x2+···+a2nxn=b2,(3.3)JJ············II(1)(1)(1)(1)an1x1+an2x2+···+a1nxn=bn.JI1.L§µBackClose(1)(1)(1)(1)(1)(1)(1)(1)(1)(1)aaa···abaaa···ab1112131n11112131n1(1)(1)(1)(1)(1)(2)(2)(2)(2)aaa···ab0aa···ab福建师范大学2122232n222232n2数计学院a(1)a(1

17、)a(1)···a(1)b(1)→0a(2)a(2)···a(2)b(2)3132333n332333n36/15························(1)(1)(1)(1)(1)(2)(2)(2)(2)an1an2an3···annbn0an2an3···annbn(1)(1)(1)(1)(1)aaa···ab1112131n1(2)(2)(2)(2)0a22a23···a2nb2→···→00a(3)···a(3)b(3)JJ333n3··

18、··········II(n)(n)J000···annbnIBackCloseÙ¥(1)(2)(1)(1)(2)(1)(1)ai1aij=aij−mi1a1j,bi=bi−mi1b1,mi1=(1),i,j=2,···,n.a福建师范大学11数计学院/,7/15(k)(k+1)(k)(k)(k+1)(k)(k)aikaij=aij−mikakj,bi=bi−mikbk,mik=(k),akki,j=k+1,···,n;k=1,···,n−1.(3.4)2.£L§µJJa(1)x+a(1)x+···+a(1)x=b

19、(1),II1111221nn1(2)(2)(2)a22x2+···+a2nxn=b2,J············I(n)(n)Backannxn=bn,Closex=b(n)(n)nn/ann,Pn(k)(k)(k)=⇒xk=bk−ak