Package org.drip.numerical.linearalgebra

Class GershgorinDisc

java.lang.Object
org.drip.numerical.linearalgebra.GershgorinDisc
public class GershgorinDisc
extends java.lang.Object
GershgorinDisc contains the diagonal entry and the "Radius" of a Row of a Square Matrix. The References are:

  • Golub, G. H., and C. F. van Loan (1996): Matrix Computations 3rd Edition Johns Hopkins University Press Baltimore MD
  • Horn, R. A., and C. R. Johnson (2013): Matrix Analysis 2nd Edition Cambridge University Press Cambridge UK
  • Li, C. K., and F. Zhang (2019): Eigenvalue Continuity and Gershgorin’s Theorem Electronic Journal of Linear Algebra 35 619-625
  • Trefethen, L. N., and D. Bau III (1997): Numerical Linear Algebra Society for Industrial and Applied Mathematics Philadelphia PA
  • Wikipedia (2024): Gershgorin Circle Theorem https://en.wikipedia.org/wiki/Gershgorin_circle_theorem




Author:
Lakshmi Krishnamurthy

  • Field Summary

    Fields
    Modifier and Type Field Description
    static double ABSOLUTE_TOLERANCE_DEFAULT
    Default Absolute Tolerance
    static double RELATIVE_TOLERANCE_DEFAULT
    Default Relative Tolerance

  • Constructor Summary

    Constructors
    Constructor Description
    GershgorinDisc​(double diagonalEntry, double radius, boolean isDiagonallyDominant)
    GershgorinDisc Constructor

  • Method Summary

    Modifier and Type Method Description
    double diagonalEntry()
    Retrieve the Diagonal Entry
    static GershgorinDisc FromRow​(double[] row, int diagonalIndex, R1ClosenessVerifier r1ClosenessVerifier)
    Construct an Instance of GershgorinDisc from the Square Matrix's Row
    boolean isDiagonallyDominant()
    Indicate if the Row is Diagonally Dominant
    double leftEdge()
    Retrieve the Disc Left Edge
    double radius()
    Retrieve the Gershgorin Disc Radius
    double rightEdge()
    Retrieve the Disc Right Edge

    Methods inherited from class java.lang.Object

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

  • Field Details

    • ABSOLUTE_TOLERANCE_DEFAULT

      public static final double ABSOLUTE_TOLERANCE_DEFAULT
      Default Absolute Tolerance
      See Also:
      Constant Field Values

    • RELATIVE_TOLERANCE_DEFAULT

      public static final double RELATIVE_TOLERANCE_DEFAULT
      Default Relative Tolerance
      See Also:
      Constant Field Values

  • Constructor Details

    • GershgorinDisc

      public GershgorinDisc​(double diagonalEntry, double radius, boolean isDiagonallyDominant) throws java.lang.Exception
      GershgorinDisc Constructor
      Parameters:
      diagonalEntry - Diagonal Entry
      radius - Radius
      isDiagonallyDominant - TRUE - The Row is Diagonally Dominant
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

  • Method Details

    • FromRow

      public static final GershgorinDisc FromRow​(double[] row, int diagonalIndex, R1ClosenessVerifier r1ClosenessVerifier)
      Construct an Instance of GershgorinDisc from the Square Matrix's Row
      Parameters:
      row - Square Matrix Row
      diagonalIndex - Diagonal Element Index
      r1ClosenessVerifier - R1ClosenessVerifier Instance
      Returns:
      GershgorinDisc Instance

    • radius

      public double radius()
      Retrieve the Gershgorin Disc Radius
      Returns:
      Gershgorin Disc Radius

    • diagonalEntry

      public double diagonalEntry()
      Retrieve the Diagonal Entry
      Returns:
      Diagonal Entry

    • isDiagonallyDominant

      public boolean isDiagonallyDominant()
      Indicate if the Row is Diagonally Dominant
      Returns:
      TRUE - The Row is Diagonally Dominant

    • leftEdge

      public double leftEdge()
      Retrieve the Disc Left Edge
      Returns:
      Disc Left Edge

    • rightEdge

      public double rightEdge()
      Retrieve the Disc Right Edge
      Returns:
      Disc Right Edge