实验三 MATLAB的数值运算
一、实验目的
1．学习MATLAB的基本矩阵运算； 2．学习MATLAB的点运算；
3．学习复杂运算。
二、实验基本知识
1.基本矩阵运算； 2.多项式运算； 3.代数方程组； 4.数值微积分。
三、上机练习
1. 给a,b,c赋如下数据:
?134?a???51244???784?,b??122438?,c?[1,0,8,3,6,2,?4,23,46,6]????53??7827????68??1)求a+b,a*b,a.*b,a/b,a./b,a^2,a.^2的结果.
2)求c中所有元素的平均值、最大值.
3)求d=b(2:3,[1,3]).
a=[1 3 4;5 12 44;7 8 27] b=[-7 8 4;12 24 38;68 -5 3] c=[1 0 8 3 6 2 -4 23 46 6]
a =
1 3 4 5 12 44 7 8 27 b =
-7 8 4 12 24 38 68 -5 3 c =
1 0 8 3 6 2 -4 23 46 6
a1=a+b a2=a*b a3=a.*b
a4=a/b a5=a./b a6=a^2 a7=a.^2
a1 =
-6 11 8 17 36 82 75 3 30 a2 =
301 60 130 3101 108 608 1883 113 413 a3 =
-7 24 16 60 288 1672 476 -40 81 a4 =
0.0966 0.0945 0.0080 -3.6125 1.5838 -0.5778 -1.9917 0.9414 -0.2682 a5 =
-0.1429 0.3750 1.0000 0.4167 0.5000 1.1579 0.1029 -1.6000 9.0000 a6 =
44 71 244 373 511 1736 236 333 1109 a7 =
1 9 16 25 144 1936 49 64 729 av=mean(c) am=max(c)
av =
9.1000 am =
46
d=b(2:3,[1,3])
d =
12 38 68 3
?123??1??X??0?，并对所得结果作出解释。 4562.求解方程????????789???0??A=[1 2 3;4 5 6;7 8 9]
B=[1;0;0]
A =
1 2 3
4 5 6 7 8 9 B = 1 0 0
x=A\\B
Warning: Matrix is close to singular or badly scaled.
Results may be inaccurate. RCOND = 1.541976e-018. x =
1.0e+015 * -4.5036 9.0072 -4.5036 R1=rank(A,B) R2=rank(A)
R1 = 3 R2 = 2
因为系数矩阵的秩R2 3.已知有理分式R(x)? N(x)3，其中N(x)?(3xD(x)?x)(x3?0.5)， D(x)?(x2?2x?2)(5x3?2x2?1)。求该分式的商多项式和余多项式。 format rat n=conv([3,0,1,0],[1,0,0,0.5]) d=conv([1,2,-2],[5,2,0,1]) [q,r]=deconv(n,d) n = Columns 1 through 5 3 0 1 3/2 0 Columns 6 through 7 1/2 0 d = Columns 1 through 5 5 12 -6 -3 2 Column 6 -2 q = 3/5 -36/25 r = Columns 1 through 5 0 0 547/25 -267/50 -138/25 Columns 6 through 7 229/50 -72/25 cq='商多项式为 '; cr='余多项式为 '; disp([cq,poly2str(q,'s')]),disp([cr,poly2str(r,'s')]) 商多项式为 0.6 s - 1.44 余多项式为 21.88 s^4 - 5.34 s^3 - 5.52 s^2 + 4.58 s - 2.88 4.求解Lorenz模型的状态方程，并图示. 初值在(0,1)中取值 global a b c a=16;b=4;c=45; lorenz=@(t,x)[a*(x(2)-x(1));c*x(1)-x(2)-x(1)*x(3);x(1)*x(2)-b*x(3)]; [t,Y]=ode45(lorenz,[0,0.5],[0.1;0.2;0.3]) t = 0 49/20824 49/10412 97/13741 49/5206 131/6806 151/5192 203/5216 407/8348 113/1875 117/1630 166/1993 104/1097 523/4874 807/6736 557/4210 85/587 2621/16662 442/2603 307/1684 2197/11278 193/931 202/919 489/2105 1649/6736 502/1951 344/1275 544/1927 278/943 408/1351 1157/3742 585/1849 365/1128 345/1043 413/1222 282/817 784/2225 455/1272 1181/3253 725/1968 1927/5156 3527/9304 953/2479 587/1506 680/1721 541/1347 531/1301 741/1787 1261/2994 560/1301 587/1335 541/1205 532/1161 1264/2697 367/766 375/766 1/2 Y = 1/10 1/5 3/10 222/2137 883/4200 409/1376 298/2759 2311/10463 311/1056 353/3141 215/927 260/891 174/1487 102/419 181/626 67/481 368/1239 86/309 533/3194 780/2161 1061/3958 683/3403 719/1643 2913/11272 202/835 469/885 1465/5872 473/1569 595/898 727/3028 881/2343 1063/1284 811/3494 1748/3725 4580/4429 399/1765 215/367 691/535 313/1405 589/790 1738/1057 88/393 1631/1719 4353/2080 205/883 2421/2005 269/101 311/1235 919/598 5267/1554 239/824 354/181 1962/455 508/1417 7057/2836 6860/1251 905/1914 3472/1097 223/32 53/80 21966/5459 2707/306 1175/1204 787/154 3978/355 1911/1283 3747/578 3356/237 1896/821 2593/316 3580/201 2638/729 2411/233 5089/229 1260/221 3823/295 2928/107 4081/457 5684/353 10028/303 5426/391 5073/257 3070/79 2679/127 3385/143 9359/215 10319/333 4045/156 12044/267 4703/124 3169/113 18212/401 10155/223 3376/113 14477/328 5347/100 7725/247 7849/191 9124/149