determine whether an iterative approximation method converges or not - Maple Help

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Student[NumericalAnalysis][IsConvergent] - determine whether an iterative approximation method converges or not

Calling Sequence

IsConvergent(A, meth)

Parameters

A

-

Matrix; a square nxn matrix

meth

-

equation; the method in the form method = one of: gaussseidel, jacobi or SOR(numeric)

Description

• 

The IsConvergent command determines whether the iterative approximation to the linear system A.x=b, using meth as the approximation method, converges to a unique solution or not, for any initial approximate.

• 

The IsConvergent command returns true or false depending on whether the method and system converge to a unique solution or not.

Examples

withStudent[NumericalAnalysis]:

A:=Matrix1.3,1.4,5.3,3.4,7.7,3.1,4.3,7.4,0.2

A:=1.31.45.33.47.73.14.37.40.2

(1)

IsConvergentA,method=gaussseidel

false

(2)

IsConvergentA,method=jacobi

false

(3)

B:=Matrix1,0,0,1

B:=1001

(4)

IsConvergentB,method=gaussseidel

true

(5)

IsConvergentB,method=jacobi

true

(6)

IsConvergentB,method=SOR1.25

true

(7)

See Also

Student[LinearAlgebra], Student[NumericalAnalysis], Student[NumericalAnalysis][ComputationOverview], Student[NumericalAnalysis][IterativeApproximate], Student[NumericalAnalysis][IterativeFormula]


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