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1、1nÙ5§
2、ê) ÙÌSNµGauss{•Gauss{§GaussÌ{§
3、5Ø©Û•þÚÝꧧ
4、5ÚØO5§
5、S{SK•JacobiS!Gauss-SeidelSª§Âñ5O¯Ì•{Ú{IKJJIIJI1155£ ¶w«'4òÑDepartmentofMathematics,SoutheastUniversity,20111Gauss{gµ
6、^5ê¥ÆSLÐ 1Cò§
7、z dn/§
8、.Gauss{1.1n/§
9、£{§
10、5Ø©Û5§
11、S{Än/§
12、SKu11x1+u12x2+···+u1,n−1xn−1+u1nxn=
13、y1¯Ìu22x2+···+u2,n−1xn−1+u2nxn=y2...·········IKun−1,n−1xn−1+un−1,nxn=yn−1JJIIunnxn=ynJIÙ¥uii6=0(i=1,2,···,n).^e¡£{¦):1255x=y/u,£nnnnXn ¶w«y/uxi=i−uijxjii,i=n−1,n−2,···,1.'4j=i+1òÑDepartmentofMathematics,SoutheastUniversity,20111.2Gauss{Ä5§
14、Ax=b,(1)Gauss{§
15、5Ø©ÛÙ¥5§
16、S{a11
17、a12···a1nx1b1SKA=a21a22···a2n,x=x2,b=b2...................¯Ìan1an2···annxnbnIKò§Ax=b^O2ÝL«,PJJII(1)(1)(1)(1)a11a12···a1na1,n+1JI(1)(1)(1)(1)A¯(1)a21a22···a2na2,n+11355=..........,.....£(1)(1)(1)(1)an1an2···annan,n+1 ¶w«Ù¥'4(1)aij=aij,i,j=1,2···n,òÑ(1)ai,n+1=b
18、i,i=1,2···,n.DepartmentofMathematics,SoutheastUniversity,2011e¡^n−1ڣР1C¤òÝA¯(1)zþnÝ.(1)1)1111ÚÚÚµµµba116=0(ÄKü1),Pli1=Gauss{(1)a§
19、5Ø©Ûi1(1),111¦−li111i(2≤i≤n)15§
20、S{a11SK(1)(1)(1)(1)aa···aa11121n1,n+1¯Ì(2)(2)(2)A¯(1)−→A¯(2)=0a22···a2na2,n+1IK...............(2)(2
21、)(2)JJII0an2···annan,n+1JIÙ¥1455(2)(1)(1)aij=aij−li1a1j,i=2,3,···,n,j=2,3,···,n+1.£(2) ¶w«2)1112ÚÚÚµµµba226=0(ÄKü1),Pli2='4òÑDepartmentofMathematics,SoutheastUniversity,2011(2)ai2,121¦−li21i(3≤i≤n)1(2)a22Gauss{(1)(1)(1)(1)(1)aaa···aa1112131n1,n+1§
22、5Ø©Û(2)(2)(2)(2)0aa··
23、·aa5§
24、S{22232n2,n+1A¯(2)−→A¯(3)=(3)(3)(3)SK00a33···a3na3,n+1..................¯Ì(3)(3)(3)00a3n···annan,n+1IKÙ¥JJII(3)(2)(2)JIaij=aij−li2a2j,i=3,4,···,n,j=3,4,···,n+1.15553)bUþ¡?1k−1Ú,=k£A¯(1)−→A¯(2)−→A¯(3)−→···−→A¯(k), ¶w«'4òÑDepartmentofMathematics,SoutheastUniversity,2011
25、Ù¥A¯(k)(1)(1)(1)(1)(1)(1)(1)aaa···aa···aa1112131,k−11k1n1,n+1(2)(2)(2)(2)(2)(2)Gauss{0aa···aa···aa22232,k−12,k2n2,n+1(3)(3)(3)(3)(3)§
26、5Ø©Û00a33···a3,k−1a3k···a3na3,n+15§
27、S{......................···..SK(k−1)(k−1)(k−1)(k−1)=000···aa···aak−1,k−1k−1,k
