三元牛頓方法（非線性方程中三個未知數(shù)）

function jie = multvarnewton3(g1,g2,g3,c) e=[inf,inf,inf]; syms x y z k1=g1(x,y,z);k2=g2(x,y,z);k3=g3(x,y,z); while(norm((e-c),inf)>0.5*10^-6) f1=diff(k1,x); f2=diff(k1,y); f3=diff(k1,z); f4=diff(k2,x); f5=diff(k2,y); f6=diff(k2,z); f7=diff(k3,x); f8=diff(k3,y); f9=diff(k3,z); d(1)=subs(subs(subs(k1,x,c(1)),y,c(2)),z,c(3)); d(2)=subs(subs(subs(k2,x,c(1)),y,c(2)),z,c(3)); d(3)=subs(subs(subs(k3,x,c(1)),y,c(2)),z,c(3)); a(1,1)=subs(subs(subs(f1,x,c(1)),y,c(2)),z,c(3)); a(1,2)=subs(subs(subs(f2,x,c(1)),y,c(2)),z,c(3)); a(1,3)=subs(subs(subs(f3,x,c(1)),y,c(2)),z,c(3)); a(2,1)=subs(subs(subs(f4,x,c(1)),y,c(2)),z,c(3)); a(2,2)=subs(subs(subs(f5,x,c(1)),y,c(2)),z,c(3)); a(2,3)=subs(subs(subs(f6,x,c(1)),y,c(2)),z,c(3)); a(3,1)=subs(subs(subs(f7,x,c(1)),y,c(2)),z,c(3)); a(3,2)=subs(subs(subs(f8,x,c(1)),y,c(2)),z,c(3)); a(3,3)=subs(subs(subs(f9,x,c(1)),y,c(2)),z,c(3)); a=double(a); d=double(d); e=c; s=a\d';c=(c'-s)'; jie=c; end end

說明：輸入中g(shù)1,g2,g3為三個方程，c為初始估計

二元牛頓方法（非線性方程中二個未知數(shù)）

function jie= multvarnewton(g1,g2,c) e=[inf,inf]; syms x y k1=g1(x,y);k2=g2(x,y); while(norm((e-c),inf)>0.5*10^-6) f1=diff(k1,x); f2=diff(k1,y); f3=diff(k2,x); f4=diff(k2,y); d(1)=subs(subs(k1,x,c(1)),y,c(2)); d(2)=subs(subs(k2,x,c(1)),y,c(2)); a(1,1)=subs(subs(f1,x,c(1)),y,c(2)); a(1,2)=subs(subs(f2,x,c(1)),y,c(2)); a(2,1)=subs(subs(f3,x,c(1)),y,c(2)); a(2,2)=subs(subs(f4,x,c(1)),y,c(2)); a=double(a); d=double(d); e=c; s=a\d';c=(c'-s)'; jie=c; end end

說明：輸入中g(shù)1,g2為三個方程，c為初始估計

Broyden方法

function jie = Broyden(f,tol,x0) [m,n]=size(x0); a=eye(n); x=x0-a\f(x0); while(norm((x-x0),inf)>tol)k1=f(x)-f(x0);k2=x-x0;a=a+(k1-a*k2)*k2'/(k2'*k2);x0=x;x=x-a\f(x); end jie=x; end

說明：輸入中f為多個方程組成的列矩陣，x0為初始估計(以列向量表示)，tol為控制精度，以向量的無窮范數(shù)表示。如控制在小數(shù)點后六位則tol=0.5*10^-6。

Broyden方法2

function jie= Broyden2(f,tol,x0) [m,n]=size(x0); a=eye(n); x=x0-a*f(x0); while(norm((x-x0),inf)>tol)k1=f(x)-f(x0);k2=x-x0;a=a+((k2-a*k1)*k2'*a)/(k2'*a*k1);x0=x;x=x-a*f(x); end jie=x; end

說明：輸入中f為多個方程組成的列矩陣，x0為初始估計(以列向量表示)，tol為控制精度，以向量的無窮范數(shù)表示。如控制在小數(shù)點后六位則tol=0.5*10^-6。

總結(jié)

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