Package org.drip.numerical.linearalgebra

Class GershgorinAnalyzer

java.lang.Object

org.drip.numerical.linearalgebra.GershgorinAnalyzer

public class GershgorinAnalyzer
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 3^rd Edition Johns Hopkins University Press Baltimore MD
• Horn, R. A., and C. R. Johnson (2013): Matrix Analysis 2^nd 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

• Module = Computational Core Module
• Library = Numerical Analysis Library
• Project = Numerical Quadrature, Differentiation, Eigenization, Linear Algebra, and Utilities
• Package = Linear Algebra Matrix Transform Library

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
GershgorinAnalyzer(R1Square squareMatrix, R1ClosenessVerifier r1ClosenessVerifier)	GershgorinAnalyzer Constructor

Method Summary

Modifier and Type	Method	Description
static GershgorinAnalyzer	FromSquareMatrix(R1Square squareMatrix, boolean useRow)	Construct a GershgorinAnalyzer Instance from the SquareMatrix
GershgorinDisc[]	gershgorinDiscArray()	Retrieve the Array of GershgorinDisc
boolean	isDiagonallyDominant()	Indicate if the Discs are Diagonally Dominant
static void	main(java.lang.String[] argumentArray)
R1Square	squareMatrix()	Retrieve the Square Matrix
R1Square	Strengthen(double t)	Construct a "Gershgorin Strengthened" Square Matrix

Methods inherited from class java.lang.Object

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

Constructor Details

GershgorinAnalyzer

public GershgorinAnalyzer(R1Square squareMatrix,
R1ClosenessVerifier r1ClosenessVerifier)
                   throws java.lang.Exception

GershgorinAnalyzer Constructor

Parameters:

squareMatrix - Input Square Matrix

r1ClosenessVerifier - R¹ Closeness Verifier

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

Method Details

FromSquareMatrix

public static final GershgorinAnalyzer FromSquareMatrix(R1Square squareMatrix,
boolean useRow)

Construct a GershgorinAnalyzer Instance from the SquareMatrix

Parameters:

squareMatrix - The SquareMatrix

useRow - TRUE - Use Rows for the Analysis

Returns:

The GershgorinAnalyzer Instance

squareMatrix

public R1Square squareMatrix()

Retrieve the Square Matrix

Returns:

Square Matrix

gershgorinDiscArray

public GershgorinDisc[] gershgorinDiscArray()

Retrieve the Array of GershgorinDisc

Returns:

Array of GershgorinDisc

isDiagonallyDominant

public boolean isDiagonallyDominant()

Indicate if the Discs are Diagonally Dominant

Returns:

TRUE - The Discs are Diagonally Dominant

Strengthen

public R1Square Strengthen(double t)

Construct a "Gershgorin Strengthened" Square Matrix

Parameters:

t - Strengthener "t"

Returns:

"Gershgorin Strengthened" Square Matrix

main

public static void main(java.lang.String[] argumentArray)
                 throws java.lang.Exception

Throws:

java.lang.Exception