贝塞尔函数零点的程序（转）

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函数参数 n：贝塞尔阶数   k：要求零点的个数   kind：第几类贝塞尔函数

function x=besselzero(n,k,kind)
- c# n, o* w' g. u9 L%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
5 s: }6 Z+ D% `6 p% c%
% besselzero.m
  r4 j& {7 r2 i0 ~' U( [%
% Find first k positive zeros of the Bessel function J(n,x) or Y(n,x)
% using Halley's method.
%
% Written by: Greg von Winckel - 01/25/05
% Contact: gregvw(at)chtm(dot)unm(dot)edu
%
% M7 w4 m9 O0 O; `" X+ ~8 }+ B%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
6 c/ f0 e0 E) u; j$ e: Wk3=3*k;
; F8 l1 s0 O# m! E) vx=zeros(k3,1);
for j=1:k3
   
    % Initial guess of zeros
3 s$ w$ J" v) G    x0=1+sqrt(2)+(j-1)*pi+n+n^0.4;
! m$ Y6 U  O0 X3 ^, {   
$ J4 i9 @. T) L8 ?    % Do Halley's method
    x(j)=findzero(n,x0,kind);
    if x(j)==inf
        error('Bad guess.');
/ T! p7 _9 s2 c    end
7 I* m1 i# [7 n6 D' D   
end
x=sort(x);
6 V& R) Y% d! v, ^! y6 w. S( I% Ndx=[1;abs(diff(x))];
) h5 R; P7 B) b" H0 }( R  j' Vx=x(dx>1e-8);
4 I8 V! K: {$ _: [0 c# Wx=x(1:k);
9 P6 v: G2 T% Cfunction x=findzero(n,x0,kind)
  m, i3 }+ O! E. V1 Jn1=n+1;     n2=n*n;
$ j* P1 M8 ?* w8 y0 P1 m% Tolerance
# `: P2 {( T1 N6 L# H+ Ktol=1e-12;
% Maximum number of times to iterate
8 f4 A9 D+ N% u" IMAXIT=100;
/ ?3 t$ o5 K9 B$ u% Initial error
& L0 A$ T& q$ S. U0 c+ ^" {& verr=1;
/ \0 `; ?; ?9 riter=0;
/ f$ E) e3 P4 s6 z" awhile abs(err)>tol & iter<MAXIT
" G1 _6 @* c: m   
    switch kind
        case 1
            a=besselj(n,x0);   
            b=besselj(n1,x0);   
        case 2
            a=bessely(n,x0);
            b=bessely(n1,x0);
/ C0 Y0 z7 v+ D6 G, K& r    end
9 g1 I1 R5 Q; K            
    x02=x0*x0;
) x% L6 z3 X  w. `   
8 z# `6 P# h4 x) t, t) H* A    err=2*a*x0*(n*a-b*x0)/(2*b*b*x02-a*b*x0*(4*n+1)+(n*n1+x02)*a*a);
8 c: W7 f1 o  [5 ?   
    x=x0-err;
    x0=x;
) G9 h0 E  K7 _0 m  l    iter=iter+1;
   
end
if iter>MAXIT-1
4 G0 D1 S4 {% N# B/ ^( a    warning('Failed to converge to within tolerance. ',...
) h, @( |+ Q& ~7 j            'Try a different initial guess');
    x=inf;   
end
( l4 V, C' I( `7 l) V

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naimei

看看楼主的代码。