Student[NumericalAnalysis] - Maple Programming 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 $\mathrm{nxn}$ 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

 > $\mathrm{with}\left(\mathrm{Student}[\mathrm{NumericalAnalysis}]\right):$
 > $A≔\mathrm{Matrix}\left(\left[\left[1.3,1.4,5.3\right],\left[3.4,7.7,3.1\right],\left[4.3,7.4,0.2\right]\right]\right)$
 ${A}{:=}\left[\begin{array}{ccc}{1.3}& {1.4}& {5.3}\\ {3.4}& {7.7}& {3.1}\\ {4.3}& {7.4}& {0.2}\end{array}\right]$ (1)
 > $\mathrm{IsConvergent}\left(A,\mathrm{method}=\mathrm{gaussseidel}\right)$
 ${\mathrm{false}}$ (2)
 > $\mathrm{IsConvergent}\left(A,\mathrm{method}=\mathrm{jacobi}\right)$
 ${\mathrm{false}}$ (3)
 > $B≔\mathrm{Matrix}\left(\left[\left[1,0\right],\left[0,1\right]\right]\right)$
 ${B}{:=}\left[\begin{array}{rr}{1}& {0}\\ {0}& {1}\end{array}\right]$ (4)
 > $\mathrm{IsConvergent}\left(B,\mathrm{method}=\mathrm{gaussseidel}\right)$
 ${\mathrm{true}}$ (5)
 > $\mathrm{IsConvergent}\left(B,\mathrm{method}=\mathrm{jacobi}\right)$
 ${\mathrm{true}}$ (6)
 > $\mathrm{IsConvergent}\left(B,\mathrm{method}=\mathrm{SOR}\left(1.25\right)\right)$
 ${\mathrm{true}}$ (7)

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