用Romberg方法求解積分

./用Romberg方法求解積分,要求誤差不超過(guò)解：Romberg.m文件：function[I,step]=Romberg<f,a,b,EPS>%Romberg.m是用龍貝格公式求積分%f為被積函數(shù)%EPS為積分結(jié)果精度%a,b為積分區(qū)間的上下限%I為積分結(jié)果；step為積分的子區(qū)間數(shù)m=1k=0Er=0.1H=b-aS=zeros<1,1>S<1,1>=<H/2>*<subs<sym<f>,findsym<sym<f>>,a>+subs<sym<f>,findsym<sym<f>>,b>>whileEr>EPSk=k+1f1=0H=H/2fori=1:mx=a+H*<2*i-1>f1=f1+subs<sym<f>,findsym<sym<f>>,x>endS<k+1,1>=S<k,1>/2+H*f1m=2*mforn=1:kS<k+1,n+1>=S<k+1,n>+<S<k+1,n>-S<k,n>>/<4^n-1>endEr=abs<S<k+1,n+1>-S<k,n>>endI=S<k+1,k+1>step=k命令：clearclcformatshorta=0;b=0.8;EPS=1e-2;[I,step]=Romberg<'x^<1/2>',a,b,EPS>計(jì)算結(jié)果：m=1k=0Er=0.1000H=0.8000S=0S=0.3578k=1f1=0H=0.4000x=0.4000f1=0.6325S=0.35780.4319m=2S=0.357800.43190.4566Er=0.0988k=2f1=0H=0.2000x=0.2000f1=0.4472x=0.6000f1=1.2218S=0.357800.43190.45660.46030m=4S=0.357800.43190.45660.46030.4698S=0.3578000.43190.456600.46030.46980.4707Er=0.0141k=3f1=0H=0.1000x=0.1000f1=0.3162x=0.3000f1=0.8640x=0.5000f1=1.5711x=0.7000f1=2.4077S=0.3578000.43190.456600.46030.46980.47070.470900m=8S=0.3578000.43190.456600.46030.46980.47070.47090.47450S=0.3578000.43190.456600.46030.46980.47070.47090.47450.4748S=0.35780000.43190.4566000.46030.46980.470700.47090.47450.47480.4748Er=0.0042I=0.4748step=3I=0.4748step=3設(shè)方程組試用Jacobi迭代法求解此方程,,當(dāng)時(shí)終止迭代。解：Jacobi.m文件：functionJacobi<A,b,max,eps>%max為最大迭代次數(shù),eps為容許誤差n=length<A>;x=zeros<n,1>;x1=zeros<n,1>;k=0;while1x1<1>=<b<1>-A<1,2:n>*x<2:n,1>>/A<1,1>fori=2:n-1x1<i>=<b<i>-A<i,1:i-1>*x<1:i-1,1>-A<i,i+1:n>*x<i+1:n,1>>/A<i,i>endx1<n>=<b<n>-A<n,1:n-1>*x<1:n-1,1>>/A<n,n>k=k+1ifsum<abs<x1-x>><epsfprintf<'number=%d\n',k>breakendifk>=maxfprintf<'TheMethodisdisconvergent\n'>breakendx=x1endifk<maxfori=1:nfprintf<'x[%d]=%f\n',i,x1<i>>endend命令：clearclcformatshortA=[521;-142;2-310];b=[-12203]';max=100;eps=1e-5Jacobi<A,b,max,eps>計(jì)算結(jié)果：i=1A=521-1422-310b=-12203D=5000400010L=000100-230U=0-2-100-2000D0=0.20000000.25000000.1000x0=000B=0-0.4000-0.20000.25000-0.5000-0.20000.30000f=-2.40005.00000.3000x=-2.40005.00000.3000x0=-2.40005.00000.3000i=2x=-4.46004.25002.2800x0=-4.46004.25002.2800i=3x=-4.55602.74502.4670x0=-4.55602.74502.4670i=4x=-3.99142.62752.0347x0=-3.99142.62752.0347i=5x=-3.85792.98481.8865x0=-3.85792.98481.8865i=6x=-3.97123.09221.9670x0=-3.97123.09221.9670i=7x=-4.03033.02372.0219x0=-4.03033.02372.0219i=8x=-4.01392.98152.0132x0=-4.01392.98152.0132i=9x=-3.99522.99001.9972x0=-3.99522.99001.9972i=10x=-3.99543.00261.9960x0=-3.99543.00261.9960i=11x=-4.00023.00311.9999x0=-4.00023.00311.9999i=12x=-4.00123.00002.0010x0=-4.00123.00002.0010i=13x=-4.00022.99922.0002x0=-4.00022.99922.0002i=14x=-3.99972.99981.9998x0=-3.99972.99981.9998i=15x=-3.99993.00021.9999x0=-3.99993.00021.9999i=16x=-4.00003.00012.0000x0=-4.00003.00012.0000i=17x=-4.00003.00002.0000x0=-4.00003.00002.0