實(shí)驗(yàn)八 數(shù)據(jù)分析與多項(xiàng)式計(jì)算

1、閩江學(xué)院電子系實(shí)驗(yàn)報(bào)告學(xué)生姓名：班級(jí)：學(xué)號(hào)：課程：MATLAB程序設(shè)計(jì)一、實(shí)驗(yàn)題目：數(shù)據(jù)分析與多項(xiàng)式計(jì)算二、實(shí)驗(yàn)地點(diǎn)：A210三、實(shí)驗(yàn)?zāi)康?1、掌握數(shù)據(jù)統(tǒng)計(jì)和分析的方法；2、掌握數(shù)據(jù)插值和曲線擬合的方法及其應(yīng)用；3、掌握多項(xiàng)式的常用運(yùn)算。四、實(shí)驗(yàn)內(nèi)容：1、產(chǎn)生一個(gè)5x5的隨機(jī)矩陣，進(jìn)行以下數(shù)據(jù)處理：（1）分別計(jì)算每行的最大值，每列的最大值和矩陣的最大元素；（2）分別計(jì)算每行元素的乘積，每列元素的乘積和全部元素的乘積;（3）計(jì)算每行的平均值和每列的中間值。2、產(chǎn)生一個(gè)3x4的隨機(jī)矩陣，從不同維方向求出其標(biāo)準(zhǔn)方差。3、按下表所示用3次多項(xiàng)式方法插值計(jì)算1100之間整數(shù)的平方根。表8-1 1100之

2、間特殊值的平方根表N149162536496481100123456789104、在上題中，對(duì)表格內(nèi)數(shù)據(jù)做5次多項(xiàng)式擬合，然后計(jì)算1100之間整數(shù)的平 方根值，與上題結(jié)果做比較。5、有三個(gè)多項(xiàng)式P(x) = x4 + 2x3+ 4x2+5，P(x) = x + 2，P(x) = x2 + 2x + 3，試進(jìn)行以下操作：求 P (x) = A=fix(20*rand(5)A =3139131413717666171651610171261131116107 max(A,2)ans =1417171716 max(A)ans =1317171316 max(max(A) ans =17(2) pr

3、od(A,2)ans =638825569213056013464036960 prod(A,1)ans =702028928947001623400103488 prod(prod(A,1)ans =2.3115e+024(3) mean(A,2)ans =10.40009.800012.000011.20009.4000 median(A)ans =613166112、產(chǎn)生一個(gè)3 4的隨機(jī)矩陣，從不同維方向求出其標(biāo)準(zhǔn)方差。 B=fix(20*rand(3,4)B = TOC o 1-5 h z 141319310121019815175 y1=std(B,0,1)y1 =3.05511.5

4、2754.72588.7178 y2=std(B,1,1)y2 =2.49441.24723.85867.1181 y3=std(B,0,2)y3 =6.70204.27205.6789 y4=std(B,1,2) y4 =5.80413.69974.91813、用3次多項(xiàng)式方法插值計(jì)算1100之間整數(shù)的平方根。 N=1,4,9,16,25,36,49,64,81,100;Y=1,2,3,4,5,6,7,8,9,10;X=1:100;interp1(N,Y,X,cubic)ans =1.00003.00004.12371.37293.16364.24351.71253.31864.35992.

5、00002.24052.45513.46613.60693.74224.47304.58324.69072.64943.87294.79582.82924.00004.89885.00005.09935.19665.29215.38575.47775.56815.65705.74465.83095.91606.00006.08296.16476.24546.32496.40356.48106.55776.63346.70826.78236.85566.92817.00007.07127.14167.21137.28047.34877.41647.48357.55007.61597.68127.

6、74597.81027.87397.93728.00008.06238.12428.18558.24648.30688.36688.42638.48548.54418.60248.66038.71788.77498.83178.88818.94429.00009.05559.11079.16559.22019.27449.32849.38219.43549.48849.54129.59359.64569.69739.74869.79969.85029.90059.950510.00004、在上題中，對(duì)表格內(nèi)數(shù)據(jù)做5次多項(xiàng)式擬合，然后計(jì)算1100之間整數(shù) 的平方根值，與上題結(jié)果做比較。 p=po

7、lyfit(N,Y,5)P =0.0000-0.00000.0002-0.00930.31480.7733 T=1:100; polyval(p,T)ans =1.07901.36711.63861.89462.13602.36362.57842.78122.97283.15393.32523.48763.64153.78773.92674.05924.18564.30644.42224.53344.64054.74374.84354.94035.03435.12605.21545.30305.38905.47355.55675.63895.72025.80085.88075.96016.03

8、906.11766.19606.27416.35206.42976.50736.58476.66206.73916.81606.89276.96927.04547.12127.19677.27177.34617.42017.49347.56597.63787.70887.77897.84807.91617.98328.04918.11398.17748.23978.30068.36038.41868.47568.53138.58578.63878.69058.74118.79058.83898.88628.93278.97849.02359.06829.11259.15679.20109.24

9、579.29109.33719.38439.43319.48379.53649.59189.65019.71199.77769.84779.922710.0033由實(shí)驗(yàn)結(jié)果可知，數(shù)值插值所獲得的數(shù)據(jù)沒有比曲線擬合所獲得的數(shù)據(jù)準(zhǔn)確5、有三個(gè)多項(xiàng)式 P(x) = x 4 + 2 x 3 + 4x2+5，P (x) = x + 2，P (x) = x 2 + 2 x + 3，試進(jìn)行以下操作:求 P (x) = P( x) + p(x) P3(x)P1=1,2,4,0,5; P2=1,2; P3=1,2,3; A=conv(P2,P3)A =1476 A=0,1,4,7,6; P=P1+AP =138

10、711求P(x)的根 x=roots(P)x =-1.3840 + 1.8317i-1.3840 - 1.8317i-0.1160 + 1.4400i-0.1160 - 1.4400i七、實(shí)驗(yàn)結(jié)果：1、什么是數(shù)據(jù)插值？什么是曲線擬合？說明它們的共同點(diǎn)和不同點(diǎn)。數(shù)據(jù)插值：在離散數(shù)據(jù)的基礎(chǔ)上補(bǔ)插連續(xù)函數(shù)，使得這條連續(xù)曲線通過全部給定的離散數(shù)據(jù) 點(diǎn)。插值是離散函數(shù)逼近的重要方法，利用它可通過函數(shù)在有限個(gè)點(diǎn)處的取值狀況，估算出 函數(shù)在其他點(diǎn)處的近似值。曲線擬合：推求一個(gè)解析函數(shù)y=f(x)使其通過或近似通過有限序列的資料點(diǎn)(xi, yi),通常用 多項(xiàng)式函數(shù)通過最小二乘法求得此擬合函數(shù)。數(shù)據(jù)插值，曲線

11、擬合的目的都是用一個(gè)較簡(jiǎn)單的函數(shù)去逼近一個(gè)復(fù)雜的或未知的函數(shù)，所依 據(jù)的條件都是在一個(gè)區(qū)間或一個(gè)區(qū)域上的有限個(gè)采樣點(diǎn)的函數(shù)值。數(shù)據(jù)插值要求逼近函數(shù)在 采樣點(diǎn)與被逼近函數(shù)相等。曲線擬合是構(gòu)造函數(shù)y=g(x)去逼近f(x)，但它放棄在插值點(diǎn) 兩者完全相等的要求，使其在某種意義下最優(yōu)化。曲線擬合的最優(yōu)標(biāo)準(zhǔn)是采用常見的最小二 乘原理。所構(gòu)造的g(x)是一個(gè)次數(shù)小于插值節(jié)點(diǎn)個(gè)數(shù)的多項(xiàng)式。2、利用MATLAB提供的rand函數(shù)生成30000個(gè)符合均勻分布的隨機(jī)數(shù)，然后檢驗(yàn)隨機(jī)數(shù)的性質(zhì)：均值和標(biāo)準(zhǔn)方差； x=rand(1,30000); mean(x)ans =0.5026 std(x)ans =0.289

12、9最大元素和最小元素； max(x)ans =1.0000 min(x)ans =1.5584e-005大于0.5的隨機(jī)數(shù)個(gè)數(shù)占總數(shù)的百分比。 n=0;for i=1:30000if(x(i)0.5)n=n+1;endend nn =15131 y=n/30000y =0.50443、已知lg(x)在1,101區(qū)間11個(gè)整數(shù)采樣點(diǎn)的函數(shù)值如表8-2所示。試求lg(x)的5次擬合多項(xiàng)式p(x)，并繪制出lg(x)和 p(x)在1,101區(qū)間的函數(shù)曲線。表8-2 lg(x)在11個(gè)采樣點(diǎn)的函數(shù)值x1112131415161718191101lg(01.041.321.491.611.701.781.851.901.952.00 x)14221428765313859043 x=1 11 21 31 41 51 61 71 81 91 101; y=0 1.0