实验5线性代数方程组的数值解法Word格式文档下载.docx

1、,k+1）+f2;A1=3.*eye（20,20）;A2=sparse（1:19,2:20,-1/2,20,20）;A3=sparse（1:18,3:20,-1/4,20,20）;AA=A1+A2+A3+A2+A3;A=full（AA）;b=ones（20,1）; %输入自选右端项向量bx0=ones（20,1）; %输入自选初始向量x0m=1e-5;x1=Jacob（x0,A,b,m）;x2=Gauss（x0,A,b,m）;结果输出数据：k1234567x各分量0.5833330.5277780.4994210.4895830.4851390.4832390.4823740.750.6388

2、890.6024310.5860340.5791620.5760460.5746390.8333330.7152780.6701390.6495950.6405450.6363960.6344870.7430560.6932870.6715860.6611850.65640.6541370.7042820.6817130.6709150.6657180.6632380.7077550.6855710.6747160.6693670.6667680.7083330.6870660.6762720.6709240.6682740.6874520.676850.6715350.6688830.687

3、50.6770390.6717670.6691270.6770790.6718440.6692189101112131415x各分量值0.481980.4817980.4817130.4816720.4816530.4816440.481640.4816380.5739880.5736860.5735430.5734760.5734440.5734290.5734210.5734180.6335970.6331790.6329810.6328870.6328430.6328210.6328110.6328060.6530710.6525650.6523240.6522080.6521530.6

4、521260.6521130.6521070.6620480.6614770.6612020.6610690.6610050.6609740.6609590.6609520.6655040.664890.6645910.6644460.6643760.6643410.6643250.6643160.6669720.6663330.6660190.6658650.665790.6657530.6657350.6657270.6675650.6669130.666590.6664310.6663530.6663140.6662950.6662860.6678060.6671480.6668210.

5、6666590.6665780.6665390.6665190.666510.667890.667230.6669010.6667380.6666570.6666170.6665970.6665873.3改变迭代初始值3.3.1将x0各分量初值置为0增加一句代码为:x0=zeros（20,1）;0.3333330.4166670.4537040.4689430.4758230.4789280.4722220.5526620.5637860.5689110.50.5717590.6045520.6195670.6265590.5810190.6184410.6361560.6444990.623

6、650.6430040.6523080.6248070.6450620.6549470.6250.6456890.6558830.6458170.6561620.6458330.6562350.6562490.4803650.4810350.481350.4814990.481570.4816040.4816210.571290.5724060.5729330.5731840.5733040.5733610.5733890.6298380.6313880.6321240.6324760.6326440.6327250.6327640.6484660.6503560.6512610.651696

7、0.6519050.6520060.6520550.6567780.6589310.659970.6604720.6607150.6608330.6608910.6597530.6620920.6632290.6637830.6640520.6641840.6642480.6608970.6633560.6645610.6651520.6654410.6655820.6656520.6612860.6638180.6650670.6656820.6659850.6661340.6662070.6614130.6639840.6652580.6658880.6661990.6663520.666

8、4280.6614470.6640350.665320.6659570.6662720.6664270.666504160.4816280.4816320.4816340.5734020.5734090.5734120.6327830.6327920.6327970.6520790.652090.6520960.6609180.6609320.6609390.6642790.6642940.6643020.6656860.6657020.665710.6662420.666260.6662690.6664650.6664830.6664920.6665410.666560.666569【分析】

9、从数据中可以看出，当迭代的初值变化了，达到相同精度所需要的迭代次数也变化了。3.3.2将各分量初始值置为10直接在下面给出数据结果2.8333331.5277780.910880.6753470.5689780.5220364.52.1388891.2743060.8863810.7175440.6402585.3333332.6527781.5555561.0549770.8293470.7249222.9305561.7037041.1498840.8864450.7635051.7928241.2042820.9221080.7864141.8275461.2324460.9416070

10、.7991541.8333331.245660.9515170.8062921.2495180.9561470.8098931.250.9578910.8115580.9582930.8122010.5004530.4904920.4858280.4836320.482590.4820940.4818560.6047850.5882290.5804540.5767750.5750250.5741890.5737880.6763310.6534790.6426720.6375310.6350750.6338970.6333310.7051740.6775090.6642990.6579760.6

11、549370.6534730.6527660.7213780.6900960.6750370.6677680.6642540.6625520.6617260.7299010.6962110.6798360.671870.6679940.6661050.6651850.7346720.699520.6822740.6738250.6696870.6676610.6666690.7372550.7012870.683520.674760.6704460.6683240.6672820.7385570.7022020.6841550.6752150.6707960.6686150.667540.7390810.702590.6844230.6754030.6709340.6687250.6676350.