# 幾個數值分析的演算法例子

<%
'幾個參考點的資料已經給出，輸入參數只有 X

function view(result,inputx)'輸出結果，同時如果<1 and >0,就在前面補0
if result<1 and result>0 then result=0&result
Response.Write "計算結果："&"<br>"
Response.Write "F("&inputx&")="& result
end function

'********分段線性Lagrange插值**********
function Lagrange1(inputx)
dim k,i
dim x,y
x=array("0.1","0.2","0.3","0.4")
y=array("0.0998","0.1987","0.2955","0.3894")

if inputx<x(0) then k=0
if inputx>x(3) then k=2

for i=0 to 2
if inputx>=x(i) and inputx<=x(i+1)then k=i
result=((inputx-x(k+1))/(x(k)-x(k+1)))*y(k) + ((inputx-x(k))/(x(k+1)-x(k)))*y(k+1)
next
result= view(result,inputx)
end function?

'********分段三點二次Lagrange插值**********
function Lagrange2(inputx)
dim i,j,k,t
dim x,y
result=0
x=array("0.1","0.2","0.3","0.4")
y=array("0.0998","0.1987","0.2955","0.3894")

if inputx<=x(1) then k=0
if inputx>=x(2) then k=1
if inputx>x(1) and inputx<x(2) and abs(inputx-x(1))<=abs(inputx-x(2)) then k=0 else k=1

for j=k to k+2
t=1
for i= k to k+2
if i<>j then
t= t * (inputx-x(i))/(x(j)-x(i))
end if
next
result = result + t*y(j)
next
result= view(result,inputx)
end function

'**********一元n點拉格朗日插值***********
function Lagrange3(inputx)
dim i,j
dim x,y
result=0
x=array("0","0.1","0.195","0.4","0.401","0.5")
y=array("0.39894","0.39695","0.39142","0.38138","0.36812","0.35206")

for j=0 to 5
t=1
for i=0 to 5
if i<>j then
t= t * (inputx-x(i))/(x(j)-x(i))
end if
next
result = result + t * y(j)
next
result= view(result,inputx)
end function

'***********牛頓（Newton）插值***********
function Newton(inputx)
dim x,y
dim i,j
result=0.39894
t=1
x=array("0","0.1","0.195","0.3","0.401","0.5")
y=array("0.39894","0.39695","0.39142","0.38138","0.36812","0.35206")

for j=1 to 5
t=t*(inputx - x(j-1))
for i=0 to 5-j
y(i)=(y(i+1) - y(i)) / (x(i+j) - x(i))
next
result = result + t * y(0)
next
result= view(result,inputx)
end function

'***********埃特金（Aitken）插值***********
function Aitken(inputx)
dim i,j
dim x,y
x=array("0.5","0.65","0.8","1.0")
y=array("0.4794","0.6052","0.7174","0.8415")
for j=1 to 3
for i=j to 3
y(i)=y(j-1) + (y(i)-y(j-1)) / (x(i)-x(j-1))* (inputx-x(j-1))
next
next

result= view(y(3),inputx)
end function

'***********分段兩點三次埃（厄）爾米特（Hermit）插值***********
function Hermit(inputx)
dim i,k
dim x,y,yy
x=array("0.1","0.3","0.5")
y=array("0.099833","0.295520","0.479426")
yy=array("0.995004","0.995336","0.877583")

if inputx<=x(0) then k=0
if inputx>=x(2) then k=1
for i=0 to 1
if x(i)<=inputx and inputx<=x(i+1) then k=i
next

hx1=(1+2*(inputx-x(k)) / (x(k+1)-x(k))) * mul((x(k+1)-inputx) / (x(k+1)-x(k)))
hx2=(1+2*(x(k+1)-inputx) / (x(k+1)-x(k))) * mul((inputx-x(k)) / (x(k+1)-x(k)))
hx3=(inputx - x(k))* mul((x(k+1)-inputx)/(x(k+1)-x(k)))
hx4=(inputx - x(k+1))* mul((inputx-x(k))/(x(k+1)-x(k)))

result=y(k)*hx1 + y(k+1)*hx2 + yy(k)*hx3 + yy(k+1)*hx4
result= view(result,inputx)
endfunction

function mul(str)
mul=str*str
end function

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