matlab拉格朗日插值法程序

function yh=lagrange (x,y,xh)

n = length(x)

m = length(xh)

yh = zeros(1,m)

c1 = ones(n-1,1)

c2 = ones(1,m)

for i=1:n

xp = x([1:i-1 i+1:n])

yh = yh + y(i)*prod((c1*xh-xp'*c2)./(x(i)-xp'*c2))

end

注：该程序只可一次计算实现一个插值计算。可实现多个插值计算的程序如下：

function yh=lagrange(x,y,xh)

n = length(x)

m = length(xh)

x = x(:)

y = y(:)

xh = xh(:)

yh = zeros(m,1)

c1 = ones(1,n-1)

c2 = ones(m,1)

for i=1:n,

xp = x([1:i-1 i+1:n])

yh = yh + y(i) * prod((xh*c1-c2*xp')./(c2*(x(i)*c1-xp')),2)

end

a=[3.946 05.193 505.762 1006.311 1506.795 2007.257 2507.704 3008.170 350...

8.603 4009.073 4509.511 50010.001 55010.435 60010.932 65011.400 700...

11.938 75012.428 80012.995 85013.560 90014.246 95015.063 1000]

x=a(:,2)

y=a(:,1)

x2=1:60:1200

y2=interp1(x,y,x2, 'pchip')

plot(x,y,'bo',x2,y2,'r*')

legend('千分尺数据','分段插值数据','Location', 'Best')

grid on

xlabel('x 容量值(L)'),ylabel('y 电流值（mA）')

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