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标题:
数学建模--插值和拟合实例
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作者:
血染干戈马
时间:
2018-9-13 19:41
标题:
数学建模--插值和拟合实例
数学建模--插值和拟合实例
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求导数:
- dV =
gradient(V,t);
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较为准确的插值(形成一个平滑的曲线,可以看最后一问):
pp = csape(t0,dV);fdv = ppval(pp,tt0);plot(tt0,fdv);
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拟合(polyfit和polyval)
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a = [
1
-
6
5
3
];
x
= -
5
:
0
.
3
:
5
;
y
= polyval(a,
x
);subplot(
2
,
2
,
1
);plot(
x
,
y
,
'-'
);title(
'原图形'
);L =
length
(
x
);
no
= randn(
1
,L);
%拟
合b1 = polyfit(
x
,
y
+
no
,
2
);b2 = polyfit(
x
,
y
+
no
,
3
);b3 = polyfit(
x
,
y
+
no
,
4
);y1 = polyval(b1,
x
);y2 = polyval(b2,
x
);y3 = polyval(b3,
x
);subplot(
2
,
2
,
2
);plot(
x
,y1,
'-'
);title(
'2图形'
);subplot(
2
,
2
,
3
);plot(
x
,y2,
'-'
);title(
'3图形'
);subplot(
2
,
2
,
4
);plot(
x
,y3,
'-'
);title(
'4图形'
);
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x = [1 2 3 4 5 6 7 8];y0 = [15.3 20.5 27.4 36.6 49.1 65.6 87.87 117.6];y = log(y0);b = polyfit(x,y,1);a = exp(b(2))k = (b(1)
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插值
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t
= [0 3316 6635 10619 13937 17921 21240 25223 28543 32284 35932 39332 39435 43318 44636 49953 53936 57254 60574 64554 68535 71854 75021 79254 82649 85968 89953 93270];
h
= [3175 3110 3054 2994 2947 2892 2850 2795 2752 2697 -1 -1 3550 3445 3350 3260 3167 3087 3012 2927 2842 2767 2697 -1 -1 3475 3397 3340];
t0
= t./3600;
V
= pi/4*(57*0.3024).*h*0.3024;
dV
= -gradient(V,t0);
no1
= find(h == -1);
no2
= [no1(1) - 1 : no1(2) + 1, no1(3) - 1:no1(4) + 1 ];t0(no2) = [];dV(no2) = [];
tt0
= 0:0.05:t0(end);
pp
= csape(t0,dV);
fdv
= ppval(pp,tt0);plot(tt0,fdv);
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