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NAG[f04adc] NAG[nag_complex_lin_eqn_mult_rhs] - Approximate solution of complex simultaneous linear equations with multiple right-hand sides
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Calling Sequence
f04adc(a, b, x, 'n'=n, 'nrhs'=nrhs, 'tda'=tda, 'tdb'=tdb, 'tdx'=tdx, 'fail'=fail)
nag_complex_lin_eqn_mult_rhs(. . .)
Parameters
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a - Matrix(1..n, 1..tda, datatype=complex[8], order=C_order);
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b - Matrix(1..n, 1..tdb, datatype=complex[8], order=C_order);
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x - Matrix(1..n, 1..tdx, datatype=complex[8], order=C_order);
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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  .
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Constraint:  . .
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'nrhs'=nrhs - integer; (optional)
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Default value: the second dimension of the arrays b, x.
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On entry:  , the number of right-hand sides.
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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_complex_lin_eqn_mult_rhs (f04adc) is called.
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Constraint:  . .
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'tdb'=tdb - integer; (optional)
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On entry: the second dimension of the array b as declared in the function from which nag_complex_lin_eqn_mult_rhs (f04adc) is called.
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Constraint:  . .
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'tdx'=tdx - integer; (optional)
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On entry: the second dimension of the array x as declared in the function from which nag_complex_lin_eqn_mult_rhs (f04adc) 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_complex_lin_eqn_mult_rhs (f04adc) calculates the solution of a set of complex linear equations with multiple right-hand sides.
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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 106 of Wilkinson and Reinsch (1971).
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Further Comments
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The time taken by nag_complex_lin_eqn_mult_rhs (f04adc) is approximately proportional to  .
The function may be called with the same array supplied for arguments b and x, in which case the solution vectors will overwrite the right-hand sides.
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Examples
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n := 3:
nrhs := 1:
tda := 3:
tdb := 1:
tdx := 1:
a := Matrix([[1 +0*I , 1 +2*I , 2 +10*I ], [1 +1*I , 0 +3*I , -5 +14*I ], [1 +1*I , 0 +5*I , -8 +20*I ]], datatype=complex[8], order='C_order'):
b := Matrix([[1 +0*I ], [0 +0*I ], [0 +0*I ]], datatype=complex[8], order='C_order'):
x := Matrix(3, 1, datatype=complex[8], order='C_order'):
NAG:-f04adc(a, b, x, 'n' = n, 'nrhs' = nrhs, 'tda' = tda, 'tdb' = tdb, 'tdx' = tdx):
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See Also
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Golub G H and Van Loan C F (1996) Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore
Wilkinson J H and Reinsch C (1971) Handbook for Automatic Computation II, Linear Algebra Springer–Verlag
f04 Chapter Introduction.
NAG Toolbox Overview.
NAG Web Site.
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