Examples of several numerical analysis algorithms

Algorithm <%@ Language=vbscript%>
<%
' The data for several reference points have been given, and the input parameters are only X

function view (RESULT,INPUTX) ' Outputs the result, and if <1 and >0, make up 0 in front
If Result<1 and result>0 then Result=0&result
Response.Write "Calculation result:" & "<br>"
Response.Write "F" ("&inputx&") = "& Result
End Function


' ******** piecewise linear lagrange interpolation **********
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?




' ******** piecewise 3.2 Lagrange interpolation **********
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


' ********** N-point Lagrangian interpolation ***********
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



' *********** Newton (Newton) interpolation ***********
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


' *********** Aitken (Aitken) interpolation ***********
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


' *********** 2.3-Time (Ernie) (hermit) interpolation ***********
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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