Package org.drip.numerical.linearsolver

Class RyabenkiiTsynkovScheme

java.lang.Object
org.drip.numerical.linearsolver.TridiagonalScheme
org.drip.numerical.linearsolver.PeriodicTridiagonalScheme
org.drip.numerical.linearsolver.RyabenkiiTsynkovScheme
public class RyabenkiiTsynkovScheme
extends PeriodicTridiagonalScheme
RyabenkiiTsynkovScheme 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

  • Method Summary

    Modifier and Type Method Description
    double[] solve()
    Solve the Tridiagonal System given the RHS
    static RyabenkiiTsynkovScheme Standard​(double[][] r2Array, double[] rhsArray)
    Construct a Standard Instance of RyabenkiiTsynkovScheme
    double[][] tridiagonalMatrix()
    Construct the Common U/V Tridiagonal Matrix
    double[] uRHSArray()
    Construct the U RHS Array
    double[] uSolutionArray()
    Compute the U Solution Array
    double[] uvSolver()
    Compute the Solution Array based on U/V Scheme
    double[] vRHSArray()
    Construct the V RHS Array
    double[] vSolutionArray()
    Compute the V 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

  • Method Details

    • Standard

      public static RyabenkiiTsynkovScheme Standard​(double[][] r2Array, double[] rhsArray)
      Construct a Standard Instance of RyabenkiiTsynkovScheme
      Parameters:
      r2Array - R2 Array
      rhsArray - RHS Array
      Returns:
      Standard Instance of RyabenkiiTsynkovScheme

    • tridiagonalMatrix

      public double[][] tridiagonalMatrix()
      Construct the Common U/V Tridiagonal Matrix
      Returns:
      Common U/V Tridiagonal Matrix

    • uRHSArray

      public double[] uRHSArray()
      Construct the U RHS Array
      Returns:
      U RHS Array

    • vRHSArray

      public double[] vRHSArray()
      Construct the V RHS Array
      Returns:
      V RHS Array

    • uSolutionArray

      public double[] uSolutionArray()
      Compute the U Solution Array
      Returns:
      U Solution Array

    • vSolutionArray

      public double[] vSolutionArray()
      Compute the V Solution Array
      Returns:
      V Solution Array

    • uvSolver

      public double[] uvSolver()
      Compute the Solution Array based on U/V Scheme
      Returns:
      Solution Array

    • solve

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