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Student[NumericalAnalysis]

  

MatrixConvergence

  

check whether a matrix is convergent

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

MatrixConvergence(A)

Parameters

A

-

Matrix; a square matrix

Description

• 

The MatrixConvergence command determines whether the square matrix A is convergent, in the sense that limk→Aki,j=0 for each i,j=1..n, where n is the dimension of A.

• 

A is convergent if and only if the spectral radius of A is strictly less than 1.

Examples

withStudent[NumericalAnalysis]:

AMatrix12,14,15,13,12,16,16,17,13

A:=121415131216161713

(1)

MatrixConvergenceA

true

(2)

See Also

Student[LinearAlgebra]

Student[NumericalAnalysis]

Student[NumericalAnalysis][ComputationOverview]

Student[NumericalAnalysis][SpectralRadius]

Student[NumericalAnalysis][VectorLimit]

 


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