818-6 Newton-Raphson algorithm R i=f(o Ri+0-0=0 i=f(u) Rf(U)+U-0,=0 Find the root of the equation g(x)=0 g(r=g(x)+ 1 d g(rn x-x)- 2 dx 0 Letx=xn+1--(m+1) h guess(猜测解) g(n+=g(xn)+ dg(rn) n+1 If xu+, is the root of g(x)=0 then g(xn+1=0 g(xm,) n+1 七s_g(xn or x g(xn) n+1= g(xu) If n=0 g(x0) 0 (xo --initial guess) g'(x0)
§18-6 Newton-Raphson algorithm R i i = f () − + − + s i = f () Ri + − s = 0 Rf ()+ − s = 0 Find the root of the equation g(x)=0. − + = − + = = + 2 2 2 ( ) ( ) 2! 1 ( ) ( ) ( ) ( ) n n n n n n n x x dx x x d g x x x dx x x dg x g x g x 0 Let x x n th guess n ( 1) = +1 − − + (猜测解) ( ) ( ) ( ) ( ) 1 n 1 n n n n n x x dx x x dg x g x g x − = + = + + If xn+1 i s the root of g(x) = 0 then g(xn+1 ) = 0 '( ) ( ) 1 n n n n g x g x x + − x = − '( ) ( ) 1 n n n n g x g x or x + = x − ( ) '( ) ( ) 0 0 0 0 0 1 0 x initial guess g x g x If n = xn = x x = x − − −