:ʽԤ

ʽ:
[a,b,er]=RationalFit(x,y,m,n)
[a,b,er]=RationalFit(x,y,m)
[a,b,er]=RationalFit(x,y)

x:,洢ҪϵԱ
y:,洢Ҫϵ
m:ϵaߴ,ĬΪ4
n:ϵbߴ,ĬΪ4

a:ص
b:ص
er:صϲв

˵:

1޷ȷһЩʽʽʱ,ʽϵ,Ȼϳϵ

2RationalFit(x,y,m)=RationalFit(x,y,m,m)

3xy±ʽ,Ȼϳϵab
$$
y=\dfrac{a_0+a_1x+a_2x^2+...+a_mx^m}{b_0+b_1x+b_2x^2+...+b_nx^n}
$$
4ʹñ㷨,Ҫע,ϵĴmnܸʱ,xǷȽϴ,ȽϴʱܻʹϵõĽһӰ,ʱxyݽӦٴ뱾ϡ


ԭ:

1 xy ¹ϵ
$$
y=\dfrac{a_0+a_1x+a_2x^2+...+a_mx^m}{b_0+b_1x+b_2x^2+...+b_nx^n}
$$

2ݹϵʽ֪,abͬʱһΪ0,xyӰ,ΪĹϵ,bеһΪ0,Ϊb[k],ϵʽɱʾ(b[k]=1)
$$
y=\dfrac{a_0+a_1x+a_2x^2+...+a_mx^m}{b_0+b_1x+b_2x^2+...+x^k...+b_nx^n}
$$

3ڱʽеĸΪ0ʱ,ͬʱұߵķĸԵõ

$$
x^ky = a_0 + a_1x + a_2x^2 +  + a_mx^m - b_0y - b_1xy - b_2x^2y -  - b_nx^ny
$$
4Ϊxy֪,ʽ൱ڲһСԷ鼴

PS:
㷨ҵĽһ򵥵ĳֵֵ̽δֵԶҪע⣡Ǻܸ,ɽֵΪʼֵϵн!

:

x=1:0.1:6;y=(1+2*x+3*x^2+4*x^3)/(2+3*x+4*x^2+5*x^3);//س, a = [1 2 3 4],b=[2 3 4 5]

[ar,br,er]=RationalFit(x,y,3)//سõ½,ԷĽǽabͬʱ5õĽ
ar =
[ 0.20077678201862    0.39951567103534    0.60277325466048    0.80000017332364 ]
br =
[ 0.40128583336452    0.59953553903010    0.80347077435899    1.00000000000000 ]
er =
[ 9.8735308951E-16 ]