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XLeratorDB/math Documentation

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 NameDescription
@FuncThe function to be evaluated, as a string. The function must be in the form of a SELECT statement.
@VarNameThe name of the variable
@XThe starting value for the evaluation
@DFuncA function to compute the derivative. If NULL, a numeric derivate will be computed
@MaxIterMaximum number of iterations
@tolAbsolute 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.

See Also


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