 # SQL Server NEWTON function

NEWTON
Updated: 15 April 2018

Use the scalar function NEWTON to find the root of a univariate function.

Syntax
SELECT [wct].[NEWTON] (
<@Func, nvarchar(max),>
,<@VarName, nvarchar(4000),>
,<@X, float,>
,<@DFunc, nvarchar(max),>
,<@MaxIter, int,>
,<@tol, float,>)
Arguments
 Input Name Description @Func The function to be evaluated, as a string. The function must be in the form of a SELECT statement. @VarName The name of the variable @X The starting value for the evaluation @DFunc A function to compute the derivative. If NULL, a numeric derivate will be computed @MaxIter Maximum number of iterations @tol Absolute tolerance
Return Type
[float]
Remarks
• If @Func or @Dfunc returns a NULL then NULL Is returned.
• If @Func or @Dfunc is not a valid SELECT statement then NULL is returned.
• If the derivative of x evaluates to zero, then NULL Is returned.
• If no solution is found then NULL is returned.
• If @X is NULL then @X = 0.
• If @MaxIter is NULL then @MaxIter = 100
• If @tol is NULL then @tol = 0.
• If @tol <= 0 then @tol = 0.0000000149011612
• Available in XLeratorDB / math 2008 only
Examples
Example #1

Let’s find the rout of the Legendre polynomial of degree 5.

SELECT
wct.NEWTON(
'SELECT (63 * POWER(@x,5) - 70 * POWER(@x,3) + 15 * @x)/8e+00'
,'@x'
,1.0
,NULL
,NULL
,NULL
) as newton

This produces the following result.

Example #2

Same as the previous example, except that we supply the derivate function rather than have NEWTON use a finite difference calculation.

SELECT
wct.NEWTON(
'SELECT (63 * POWER(@x,5) - 70 * POWER(@x,3) + 15 * @x)/8e+00'
,'@x'
,1.0
,'SELECT (315 * POWER(@x,4) - 210 * POWER(@x,2) + 15)/8e+00'
,NULL
,NULL
) as newton

This produces the following result.

Example #3

In this example we call the XLeratorDB PRICE function to calculate the yield on a bond using the NEWTON function and compare that with value returned by the XLeratorDB YIELD function

SELECT
wct.NEWTON(
'SELECT wct.PRICE(
''2018-04-25''
,''2025-05-15''
,.04
,@Y
,100
,2
,0) - 98.25'
,'@Y'
,.04
,NULL
,NULL
,1E-08
) as newton
,wct.YIELD(
'2018-04-25'
,'2025-05-15'
,.04
,98.25
,100
,2
,0) as yield

This produces the following result.  Copyright 2008-2021 Westclintech LLC         Privacy Policy        Terms of Service