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NAG[f04arc] NAG[nag_real_lin_eqn] - Approximate solution of real simultaneous linear equations, one right-hand side
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Calling Sequence
f04arc(a, b, x, 'n'=n, 'tda'=tda, 'fail'=fail)
nag_real_lin_eqn(. . .)
Parameters
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a - Matrix(1..n, 1..tda, datatype=float[8], order=C_order);
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b - Vector(1..n, datatype=float[8]);
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On entry: the right-hand side vector  .
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x - Vector(1..n, datatype=float[8]);
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On exit: the solution vector  .
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'n'=n - integer; (optional)
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Default value: the first dimension of the arrays a, b, x and the second dimension of the arrays a, b, xthe array a.
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On entry:  , the order of the matrix A.
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Constraint:  . .
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'tda'=tda - integer; (optional)
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On entry: the second dimension of the array a as declared in the function from which nag_real_lin_eqn (f04arc) is called.
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Constraint:  . .
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'fail'=fail - table; (optional)
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The NAG error argument, see the documentation for NagError.
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Description
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Purpose
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nag_real_lin_eqn (f04arc) calculates the approximate solution of a set of real linear equations with a single right-hand side, using an  factorization with partial pivoting.
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Error Indicators and Warnings
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"NE_ALLOC_FAIL"
Dynamic memory allocation failed.
"NE_INT_ARG_LT"
On entry, n must not be less than 1:  .
"NE_SINGULAR"
The matrix  is singular, possibly due to rounding errors.
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Accuracy
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The accuracy of the computed solution depends on the conditioning of the original matrix. For a detailed error analysis see page 107 of Wilkinson and Reinsch (1971).
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Further Comments
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The time taken by nag_real_lin_eqn (f04arc) is approximately proportional to  .
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Examples
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>
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n := 3:
tda := 3:
a := Matrix([[33, 16, 72], [-24, -10, -57], [-8, -4, -17]], datatype=float[8], order='C_order'):
b := Vector([-359, 281, 85], datatype=float[8]):
x := Vector(3, datatype=float[8]):
NAG:-f04arc(a, b, x, 'n' = n, 'tda' = tda):
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