compute an iterative formula to numerically approximate the solution to a linear system - Maple Programming Help

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Student[NumericalAnalysis][IterativeFormulaTutor] - compute an iterative formula to numerically approximate the solution to a linear system

 Calling Sequence IterativeFormulaTutor(A, b)

Parameters

 A - (optional) Matrix; a square $\mathrm{nxn}$ matrix b - (optional) Vector; a vector of length $n$

Description

 • The IterativeFormulaTutor command launches a tutor interface that takes the linear system $Ax=b$ and an initial vector ${x}_{0}$ and computes the matrix $T$ and vector $c$, of the equivalent system ${x}_{k+1}=T{x}_{k}+c$.
 • A Matrix and Vector Editors allow users to edit the matrix and vectors easily within the tutor.
 • All other available options are controlled in the tutor interface.
 • If A and b are not specified then IterativeFormulaTutor uses a default square matrix and a default vector.
 • The iterative methods available in this tutor are:
 – gaussseidel
 – jacobi
 – SOR

Notes

 • There are two digit controls in the tutor.  The Digits option controls the number of digits kept during floating-point computations, and the digit precision option controls only the number of digits to which final results are rounded in the maplet display window. The digit precision option has no effect on the output returned from the maplet upon exit.

Examples

 > $\mathrm{with}\left(\mathrm{Student}[\mathrm{NumericalAnalysis}]\right):$
 > $\mathrm{IterativeFormulaTutor}\left(\right)$
 > $\mathrm{IterativeFormulaTutor}\left(\mathrm{Matrix}\left(\left[\left[1.53,6.32\right],\left[5.33,0.33\right]\right]\right),\mathrm{Vector}\left(\left[1.66,5.66\right]\right)\right)$