Package org.drip.numerical.linearsolver

Class ShermanMorrisonScheme

java.lang.Object
org.drip.numerical.linearsolver.TridiagonalScheme
org.drip.numerical.linearsolver.PeriodicTridiagonalScheme
org.drip.numerical.linearsolver.ShermanMorrisonScheme
public class ShermanMorrisonScheme
extends PeriodicTridiagonalScheme
ShermanMorrisonScheme implements the O(n) solver for a Tridiagonal Matrix with Periodic Boundary Conditions. The References are:

  • Batista, M., and A. R. A. Ibrahim-Karawia (2009): The use of Sherman-Morrison-Woodbury formula to solve cyclic block tridiagonal and cyclic block penta-diagonal linear systems of equations Applied Mathematics of Computation 210 (2) 558-563
  • Datta, B. N. (2010): Numerical Linear Algebra and Applications 2nd Edition SIAM Philadelphia, PA
  • Gallopoulos, E., B. Phillippe, and A. H. Sameh (2016): Parallelism in Matrix Computations Spring Berlin, Germany
  • Ryaben’kii, V. S., and S. V. Tsynkov (2006): Theoretical Introduction to Numerical Analysis Wolters Kluwer Aalphen aan den Rijn, Netherlands
  • Wikipedia (2024): Tridiagonal Matrix Algorithm https://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm




Author:
Lakshmi Krishnamurthy

  • Field Summary

    Fields
    Modifier and Type Field Description
    static double BATISTA_KARAWIA_DEFAULT_GAMMA
    Batistia-Karawia Default Gamma

  • Method Summary

    Modifier and Type Method Description
    double[][] batistaKarawiaMatrix()
    Construct a Batista-Karawia Modification to the Periodic Tridiagonal Matrix
    double gamma()
    Retrieve the Gamma
    double[] qSolutionArray()
    Compute the Q Solution Array
    double[] qySolver()
    Compute the Solution Array based on Q/Y Scheme
    double[] solve()
    Solve the Periodic Tridiagonal System given the RHS
    static ShermanMorrisonScheme Standard​(double[][] r2Array, double[] rhsArray)
    Construct a Standard Gamma Instance of Sherman Morrison Solver
    static ShermanMorrisonScheme StandardBatistaKarawia​(double[][] r2Array, double[] rhsArray)
    Construct a Standard Batista-Karawia Instance of Sherman Morrison Solver
    double[] uRHSArray()
    Construct a Batista-Karawia U RHS Array
    double[] vArray()
    Construct a Batista-Karawia V Array
    double[] ySolutionArray()
    Compute the Y Solution Array

    Methods inherited from class org.drip.numerical.linearsolver.TridiagonalScheme

    matrix, rhsArray

    Methods inherited from class java.lang.Object

    equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Field Details

    • BATISTA_KARAWIA_DEFAULT_GAMMA

      public static final double BATISTA_KARAWIA_DEFAULT_GAMMA
      Batistia-Karawia Default Gamma
      See Also:
      Constant Field Values

  • Method Details

    • Standard

      public static final ShermanMorrisonScheme Standard​(double[][] r2Array, double[] rhsArray)
      Construct a Standard Gamma Instance of Sherman Morrison Solver
      Parameters:
      r2Array - R2 Array
      rhsArray - RHS Array
      Returns:
      Standard Gamma Instance of Sherman Morrison Solver

    • StandardBatistaKarawia

      public static final ShermanMorrisonScheme StandardBatistaKarawia​(double[][] r2Array, double[] rhsArray)
      Construct a Standard Batista-Karawia Instance of Sherman Morrison Solver
      Parameters:
      r2Array - R2 Array
      rhsArray - RHS Array
      Returns:
      Standard Batista-Karawia Instance of Sherman Morrison Solver

    • gamma

      public double gamma()
      Retrieve the Gamma
      Returns:
      Gamma

    • batistaKarawiaMatrix

      public double[][] batistaKarawiaMatrix()
      Construct a Batista-Karawia Modification to the Periodic Tridiagonal Matrix
      Returns:
      Batista-Karawia Modification to the Periodic Tridiagonal Matrix

    • uRHSArray

      public double[] uRHSArray()
      Construct a Batista-Karawia U RHS Array
      Returns:
      Batista-Karawia U RHS Array

    • qSolutionArray

      public double[] qSolutionArray()
      Compute the Q Solution Array
      Returns:
      Q Solution Array

    • ySolutionArray

      public double[] ySolutionArray()
      Compute the Y Solution Array
      Returns:
      Y Solution Array

    • vArray

      public double[] vArray()
      Construct a Batista-Karawia V Array
      Returns:
      Batista-Karawia V Array

    • qySolver

      public double[] qySolver()
      Compute the Solution Array based on Q/Y Scheme
      Returns:
      Solution Array

    • solve

      public double[] solve()
      Solve the Periodic Tridiagonal System given the RHS
      Specified by:
      solve in class TridiagonalScheme
      Returns:
      The Solution