第１章

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12 n x, y i 0,1,, n 1 i i y P x ) i 0, 1,, n 1 n 1 i ( i ( x x1)( x x2 ) ( x xn ) f (x) y0 ( x x )( x x ) ( x x ) ( x x0 )( x x1 ) ( x xn 1) ( x x )( x x ) ( x x ) n 2 0 n 0 1 n ( x x )( x x ) ( x x 0 2 n 1 ( x1 x0 )( x1 x2 ) ( x1 xn ) n n1 y n ) y n n x x j yi i j xi x 0 0 j i j x, y x y 9

13 x x, f x ), f ( x ),, f ( ) f ( x 1 ) f ( x 1) 0, 1, x n 1 n ( 0 1 x n s(x) f x ) c1 ( x x ) c2 ( x x ) c3 ( x x ) ( i i i i i i i xi x xi i 0, 1,, ni 2 c, c2 c3 ck 1i i i i h i 0,, n i 2 h x i i 1 x i,, d i 1,, n 2 i i i 10

14 i i i i i h h h, 1 1 i d i, i i i i i i i i h y y h y y h h , n 0 d d 1 n 0 d , ) ( 6 d n x f h y y h ) ( 6 n n n n n h y y x f h n n n n n M M M M n n d d d d M i i M ck i 0 i 2, 1,, i n i c2 i i c M 3, 2 i i i i c h M M 1, i i i i i i i h c h c h y y y x, 11

15 ( x, y0 ), ( x1, y1),, ( x n 1, yn 1) y ax b 0 y ax b n 2 S ( yi axi b) ( i 0, 1,, n i 1) i0 a, b S a b S S 2 2 axi bxi xi yi a S 2a x i b yi b 12

16 a b i n x y a n i i i i x y i i 2 x 2 x i i i i y a x i i i b n i x, y x, y y 0. 85x x y 13

17 x y 5 y (1 2 x 5 x 5 ) 14

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24 double lagrange (double nx[][50], double ny[][50], int n[], double x, int a) { } int i, j; double fx = 0, sum = 0; for (i = 0; i < n[a]; i++) { fx = ny[a][i]; for (j = 0; j < n[a]; j++) { if (i!= j) fx = fx (x - nx[a][j]) / } } sum += fx; (nx[a][i] - nx[a][j]); return (sum); j i y 21

25 double spline (double nx[][50], double ny[][50], int n[], double x, int a) { int i; double p, s; double h[1000], d[1000], f[1000], e[1000], u[1000], m[1000], end[2], c1[1000], c2[1000], c3[1000]; for (i = 0; i < n[a] - 1; i++) h[i] = nx[a][i + 1] - nx[a][i]; f[0] = 1; e[n[a] - 1] = 1; for (i = 1; i < n[a] - 1; i++) { f[i] = h[i] / (h[i - 1] + h[i]); e[i] = 1 - f[i]; u[i] = 6 / (h[i - 1] + h[i]) ((ny[a][i + 1] - ny[a][i]) / h[i] - (ny[a][i] - ny[a][i - 1]) / h[i - 1]); } for (i = 0; i < n[a]; i++) d[i] = 2; end[0] = 0; end[1] = 0; u[0] = 6 / h[0] ((ny[i][1] - ny[i][0]) / h[0] - end[0]); u[n[a] - 1] = 6 / h[n[a] - 2] (end[1] - (ny[a][n[a] - 1] - ny[a][n[a] - 2]) / h[n[a] - 2]); for (i = 0; i < n[a] - 1; i++) { } p = e[i + 1] / d[i]; d[i + 1] -= p f[i]; u[i + 1] -= p u[i]; 22

26 } u[n[a] - 1] /= d[n[a] -1]; for (i = n[a] - 2; i >= 0; i--) { u[i] = (u[i] - f[i] u[i + 1]) / d[i]; } for (i = 0; i < n[a]; i++) { } m[i] = u[i]; for (i = 0; i < n[a] - 1; i++) { c2[i] = m[i] / 2; c3[i] = (m[i+1] - m[i]) / (6 h[i]); c1[i] = (ny[a][i+1] - ny[a][i]) / h[i] - c2[i] h[i] - c3[i] h[i] h[i]; if ((x >= nx[a][i]) && (x <= nx[a][i + 1])) { s = ny[a][i] + c1[i] (x - nx[a][i]) + c2[i] (x - nx[a][i]) (x - nx[a][i]) + } } c3[i] (x - nx[a][i]) (x - nx[a][i]) (x - nx[a][i]); return (s); c1, c2 c3 i i i y 23

27 double lsq1(double nx[][50], double ny[][50], int n[], int c) { double a, b, A=0, B=0, C=0, D=0; int i; or (i = 0; i < n[c]; i++) { A += nx[c][i] ny[c][i]; B += nx[c][i]; C += ny[c][i]; D += nx[c][i] nx[c][i]; a = (n[c] A - B C) / (n[c] D - B B); b = (C - a B) / n[c]; return (a);//lsq2 b } b a a b 24

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38 //{{NO_DEPENDENCIES}} // Microsoft Developer Studio generated include file. // Used by riso.rc // #define IDC_COMBO #define IDC_COMBO

39 #define IDC_EDIT #define IDC_EDIT #define IDC_xa #define IDC_xa #define IDC_ya #define IDC_ya #define IDC_xb #define IDC_xb #define IDC_yb #define IDC_yb #define IDC_xc #define IDC_xc #define IDC_yc #define IDC_yc #define IDC_xd #define IDC_xd #define IDC_yd #define IDC_yd #define IDC_xe #define IDC_xe #define IDC_ye #define IDC_ye #define GRAPH #define DEL #define VERSION

40 #define SAVEBMP #define NEWFILE #define FILEOPEN #define SAVENAMEFILE #define SAVEFILE #define SETPRINTER #define PRINT #define EXIT #define SETGRAPH #define SETGRAPH #define SETGRAPH #define SETGRAPH #define SETGRAPH // Next default values for new objects // #ifdef APSTUDIO_INVOKED #ifndef APSTUDIO_READONLY_SYMBOLS #define _APS_NEXT_RESOURCE_VALUE 125 #define _APS_NEXT_COMMAND_VALUE #define _APS_NEXT_CONTROL_VALUE 1269 #define _APS_NEXT_SYMED_VALUE 101 #endif #endif 37

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