Newton




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CapeTools One-Dimensional Solvers function list

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Creates a One-dimensional Newton solver object to be used within the CapeTools Option Solver category of functions.

The implementation of the algorithm was inspired by Press, Teukolsky, Vetterling, and Flannery, 'Numerical Recipes in C', 2nd edition, Cambridge University Press.



This function creates an object and returns a string-key value to represent this created object.
The TAG value of the string-key returned (second part of the key) is : "Newton"



Note: Within Excel, the function is named - CT.SOLVER.Newton


High level graphic of Newton() function with parameters. Blue square node is the actual function with the parameters ordered.



Parameter Description


  1. Key parameter

    Key value to use as a handle for the created object
  2. Reload parameter

    When creating this object for the first time, set this parameter to a positive value. Within Excel, when re-computing a worksheet where you do not wish to recreate the object, set this parameter to zero (0).
  3. MaxNoOfIterations parameter

    Maximum number of iterations.
  4. LowerBound parameter

    optional lower bound value of the parameter to be solved for.
  5. UpperBound parameter

    optional upper bound value of the parameter to be solved for.


Extended information

Function Syntax

VB Syntax 


String CT1DSolvers.Newton( _
String Key, _
Long Reload, _
Long MaxNoOfIterations, _
Double LowerBound, _
Double UpperBound)


Excel Spreadsheet Syntax 


=CT.SOLVER.Newton(
Excel String Cell Key,
Excel Numeric Cell Reload,
Excel Numeric Cell MaxNoOfIterations,
Excel Numeric Cell LowerBound,
Excel Numeric Cell UpperBound)


C++ Syntax 


static std::string Newton(
std::string Key,
long Reload,
long MaxNoOfIterations,
double LowerBound,
double UpperBound);


DotNET Syntax 


System.String CT1DSolversSA.Newton(
System.String Key,
System.Int32 Reload,
System.Int32 MaxNoOfIterations,
System.Double LowerBound,
System.Double UpperBound);

Parameter data types

ArgNameArgTypeIsKey
KeyStringFALSE
ReloadLongFALSE
MaxNoOfIterationsLongFALSE
LowerBoundDoubleFALSE
UpperBoundDoubleFALSE

Example Inputs

The first column represents the name of the parameters. The second column specifies whether the parameters are optional or not. Finally the last column provides some sample input data.
Function call input string-keys are always in the format : "NAME.EXTTAG.TICKER" The "EXTTAG.TICKER" part is determined from the output of other, capetools, object creation functions.


ArgNameIsOptional (Excel only)Example
KeyFALSEMyNewton
ReloadFALSE1
MaxNoOfIterationsFALSE100
LowerBoundTRUE0.001
UpperBoundTRUE0.90


Example function usage


The C# example below contains all the sub-function calls leading up to this function call. As a result, the example can contain a lot of code.

The VB.NET, J#, C++.NET, Java, Excel VBA, Visual Basic 6 (via COM) and C++ examples below contain function code stubs for the calls leading up to this function call. However, the function call for this function is displayed.
You can easily reproduce the stub functions code from the C# example.


If you are accessing this functrion via the MiniXL libraries, this function is present within the CT.QL.Models20 MiniXL Excel Addin.

Within our Excel Example Addin Generator, we have used the following QuantTools sub-functions in order to prepare the arguments needed to call the Newton() function. If you are executing this function via the MiniXL libraries, the module addin name, (in brackets, to the right of the sub-functions listed below), indicates the MiniXL library in which the sub-function is held. You will need to load this library into your Excel session (along with any other libraries that the sub-function call within the addin requires (ie - CT.QT.Utils20 addin in almost all cases) in order for the example to compute successfully.


The following four examples demostrate calling this function within a Microsoft .NET environment

The following four examples demostrate calling this function within a non .NET environment

The following is a sample output from executing the Newton() function call


MyNewton_4.Newton.0

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