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拉格朗日、牛顿、拟合的应用
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某鄉(xiāng)鎮(zhèn)企業(yè)2010-2016年的大致生產(chǎn)利潤(rùn)如下表，試采用正確的方法預(yù)測(cè)2017和2018年的利潤(rùn)
年份 2010 2011 2012 2013 2014 2015 2016
利潤(rùn)(萬(wàn)元) 70 122 144 152 174 196 202
#include<iostream>
#include<math.h>
#include<vector>
using namespace std
;
double x
[7], y
[7];
double table
[8][8];
struct Newtoninterpolation
{Newtoninterpolation() {x
[0] = 2010, y
[0] = 70;x
[1] = 2011, y
[1] = 122;x
[2] = 2012, y
[2] = 144;x
[3] = 2013, y
[3] = 152;x
[4] = 2014, y
[4] = 174;x
[5] = 2015, y
[5] = 196;x
[6] = 2016, y
[6] = 202;}public:void Lagrangeinterpolation_solution(double _x
) {double result
=0.0, t
= 0;for (int i
= 0; i
< 7; i
++) {t
= 1;for (int j
= 0; j
< 7; j
++) {if (j
!= i
)t
*= (_x
- x
[j
]) / (x
[i
] - x
[j
]);}result
+= t
* y
[i
];}cout
<< _x
<< "的拉格朗日插值為：" <<result
<<endl
;}void Newton_solution() {for (int i
= 0; i
< 7; i
++)table
[i
][0] = y
[i
];for (int i
= 1; i
<= 7; i
++) {for (int j
= 1; j
<= i
; j
++) {table
[i
][j
] = (table
[i
][j
- 1] - table
[i
- 1][j
- 1]) / (x
[i
] - x
[i
- j
]);}}cout
<< "差商表：" << endl
;for (int i
= 0; i
< 7; i
++) {for (int j
= 0; j
<= i
; j
++) {cout
<< table
[i
][j
] << " ";}cout
<< endl
;}cout
<< "2017估計(jì)值：" << endl
;double a
= 2017, result
= 0, c
= 1;for (int i
= 0; i
< 7; i
++) {result
+= table
[i
][i
] * c
;c
*= (a
- x
[i
]);}cout
<< result
<< endl
;a
= 2018, result
= 0, c
= 1;cout
<< "2018估計(jì)值：" << endl
;for (int i
= 0; i
< 7; i
++) {result
+= table
[i
][i
] * c
;c
*= (a
- x
[i
]);}cout
<< result
<< endl
;}void fitting_process(long long _x
) {long long a
, b
;long long a1
[2][3] = { 0 }, c1
[2][3] = {0};long long r
= 0;long long r1
= 0;a1
[0][0] = 7;for (int i
= 0; i
< 7; i
++) {a1
[0][2] =a1
[0][2]+ y
[i
];a1
[1][2] =a1
[1][2]+ x
[i
] * y
[i
];}
for (int i
= 0; i
< 7; i
++) {r
=r
+ x
[i
];r1
=r1
+ (x
[i
] * x
[i
]);}a1
[0][1] = r
;a1
[1][0] = a1
[0][1];a1
[1][1]=r1
;long long k
= a1
[1][0] / a1
[0][0];for (int j
= 0; j
< 3; j
++) {a1
[1][j
] =a1
[1][j
] - a1
[0][j
] * k
;}b
= a1
[1][2] / a1
[1][1];a
=(a1
[0][2] - a1
[0][1] * b
) / a1
[0][0];cout
<< "線性擬合"<<_x
<< "年的預(yù)測(cè)是：" << a
+ b
* _x
<< endl
;}};int main() {cout
<< "1707004347--黃洪飛" << endl
;Newtoninterpolation newtoninterpolation
;newtoninterpolation
.Lagrangeinterpolation_solution(2017);newtoninterpolation
.Lagrangeinterpolation_solution(2018);newtoninterpolation
.Newton_solution();newtoninterpolation
.fitting_process(2017);newtoninterpolation
.fitting_process(2018);system("pause");return 0;
}
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