matlab在計(jì)算方法中的應(yīng)用(編輯修改稿)
2025-06-16 22:49 本頁面
【文章內(nèi)容簡介】 ater use with PPVAL, etc. Ordinarily, the notaknot end conditions are used. However, if Y contains two more ordinates than X has entries, then the first and last ordinate in Y are used as the endslopes for the cubic spline. 例：正弦函數(shù) x = 0:10。 y = sin(x)。 xx = 0:.25:10。 yy = spline(x,y,xx)。 plot(x,y,39。o39。,xx,yy) 0 2 4 6 8 101 0 . 500 . 51例：如下表所示數(shù)據(jù) x 28 29 30 f(x) x=[28 29 30]。 y=[ ]。 x0=[28::30]。 y1=spline(x,y,x0)。 plot(x,y,39。r39。) hold on plot(x0,y1) 28 2 8 . 2 2 8 . 4 2 8 . 6 2 8 . 8 29 2 9 . 2 2 9 . 4 2 9 . 6 2 9 . 8 3033 . 544 . 5最小二乘法擬合 ?在科學(xué)實(shí)驗(yàn)的統(tǒng)計(jì)方法中，往往要從一組實(shí)驗(yàn)數(shù)據(jù) (xi,yi)中尋找出自變量 x和因變量 y之間的函數(shù)關(guān)系 y=f(x)。 ?由于觀測數(shù)據(jù)往往不夠準(zhǔn)確，因此并不要求 y=f(x)經(jīng)過所有的點(diǎn) (xi,yi)，而只要求在給定點(diǎn) xi上誤差 ei=f(xi)yi按照某種標(biāo)準(zhǔn)達(dá)到最小，通常采用歐氏范數(shù) ||e||2作為誤差度量的標(biāo)準(zhǔn)，這就是最小二乘法。 MATLAB實(shí)現(xiàn) ? 利用 polyfit函數(shù)進(jìn)行多項(xiàng)式擬合 POLYFIT Fit polynomial to data. POLYFIT(X,Y,N) finds the coefficients of a polynomial P(X) of degree N that fits the data, P(X(I))~=Y(I), in a leastsquares sense. [P,S] = POLYFIT(X,Y,N) returns the polynomial coefficients P and a structure S for use with POLYVAL to obtain error estimates on predictions. If the errors in the data, Y, are independent normal with constant variance, POLYVAL will produce error bounds which contain at least 50% of the predictions. The structure S contains the Cholesky factor of the Vandermonde matrix (R), the degrees of freedom (df), and the norm of the residuals (normr) as fields. ? 利用矩陣除法解決復(fù)雜型函數(shù)的擬合 例：擬合以下數(shù)據(jù) x y ?x=[ ]。 ?y=[ ]。 ?a=polyfit(x,y,2) a = ?x1=[::]。 ?y1=a(3)+a(2)*x1+a(1)*x1.^2。 ?plot(x,y,39。*39。) ?hold on ?plot(x1,y1,39。r39。) 0 . 5 1 1 . 5 2 2 . 5 30246810例：根據(jù)經(jīng)驗(yàn)公式 y=a+bx2，擬合如下數(shù)據(jù)： xi 19 25 31 38 44 yi ?x=[19 25 31 38 44]。 ?y=
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