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1、数值分析实验报告实验一舍入误差与数值稳定性1•实验名称对n二0,1,2,...,20计算定积分yn2•实验目的学会用递推公式解定积分计算问题，并且学习将算法转换成可以运行的程序。3•算法描述算法1利用递推公式yn二片”1,2,…,20取ln6-ln5«0.182322算法2利用递推公式yn_=^yn注意到1126,112011詁X2乐彳冷lx钥x%1105取+击）“他73。4•源程序算法一:#ineludevoidmain(){floatn=1;floaty=0.182322;coutvv”y0”vv”=”vvyvvendl;for(n;n<=20;n++
2、)y=1/n-5*y;coutvv”y"vvnvv”=”vvyvvendl;}}算法二：#ineludevoidmain(){doublen=20;doubley=0.008730;coutvv”y20”vv”=”vvyvvendl;for(n;n>=0;n-){y=1/(5*n)-0.2*y;coutvv”y"vvnvv”=”vvyvvendl;}}5•运行结果算法一运行结果：y0=0.182322y1=0.08839y2=0.0580499y3=0.0430839y4=0.0345805y5=0.0270974y6=0.0311798y7=-0.013
3、0418y8=0.190209y9=-0.839935y10=4.29967y11=-21.4075y12=107.121y13=-535.526y14=2677.7y15=-13388.4y16=66942.3y17=-334711y18=1.67356e+006y19=-8.36779e+006y20=4.18389e+007Pressanykeytocontinue算法二运行结果：y20=0.00873y19=0.00878032y18=0.00935505y17=0.0098937y16=0.0105213y15=0.0112291y14=0.0120399y13=0.0
4、129766y12=0.0140713y11=0.0153676y10=0.0169265y9=0.0188369y8=0.0212326y7=0.0243249y6=0.0284684y5=0.0343063y4=0.0431387y3=0.0580389y2=0.0883922y1=0.182322Pressanykeytocontinue6•对算法的理解与分析（包括改进与建议）在程序运行过程屮，将数值定义为浮点型会“警告”，而更改为双精度类型是就不会“警告”。推断是因为参与计算的数有效数字太多,但是，忽略“警告”将得到一样的结果。实验二拉格朗日插值与牛顿插值计算机121班吴
5、珍珍122460一、目的与要求：＞熟悉拉格朗日插值多项式和牛顿插值多项式，注意其不同特点;二、实验内容：＞通过拉格朗日插值和牛顿插值多项式的两个实例的计算，了解两种求解方法，分析他们的优缺点。三、程序与实例＞拉格朗日多项式算法1.输入x,,y/(i=0,l,2,・・・,n),令L(x”)=0;2.对=0,1,2,…,n计算山r—Yn—to兀-XjL,kL“+l,(x)y,四、程序与实例例1已知函数表X：0.561600.562800.564010.565210.827410.826590.825770.82495用三次拉格朗日多项式求x=0・5635的函数近似值。源程序：#inc
6、ludevoidmain(){doublex[4]={0.56160,0.56280,0.56401,0.56521};doubley[4]={0.82741,0.82659,0.82577,0.82495};cout«H初始的X值:H«endl;for(inti=0;i<4;i++){cout«x[i]«H”；}cout«,,«H初始的Y值:n«endl;for(intj=O;j<4;j++){cout«y[j]«nn;}cout«,,;doublexn=0・5635,l[4
7、,sum=0;l[0]=(xn-x[l])*(xn-x[2])*(xm
8、x⑶)/(x[0]-x[l])/(x[0]-x[2])/(x[0]-x[3]);cout«nL0=n«lLOJ«endl;l[l]=(xn-x[0])*(xn-x[2])*(xmx⑶)/(x[l].x[0])/(x[l]-x[2])/(x[l]-x[3]);cout«nLl=n«l[1]«endl;1[2]=(xmx[0])*(xmx[l])*(xmx[3])/(x[2卜x[0])/(x[2卜x[l])/(x[2卜x[3]);cout«HL2=n«l[2]«endl;1[3]=(
