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NAG[f04agc] NAG[nag_real_cholesky_solve_mult_rhs] - Approximate solution of real symmetric positive-definite simultaneous linear equations (coefficient matrix already factorized by f03aec (nag_real_cholesky))
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Calling Sequence
f04agc(a, p, b, x, 'n'=n, 'nrhs'=nrhs, 'tda'=tda, 'tdb'=tdb, 'tdx'=tdx, 'fail'=fail)
nag_real_cholesky_solve_mult_rhs(. . .)
Parameters
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a - Matrix(1..n, 1..tda, datatype=float[8], order=C_order);
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p - Vector(1..n, datatype=float[8]);
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b - Matrix(1..n, 1..tdb, datatype=float[8], order=C_order);
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x - Matrix(1..n, 1..tdx, datatype=float[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, p, b, x and the second dimension of the arrays a, p, 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_real_cholesky_solve_mult_rhs (f04agc) 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_real_cholesky_solve_mult_rhs (f04agc) 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_real_cholesky_solve_mult_rhs (f04agc) 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_cholesky_solve_mult_rhs (f04agc) calculates the approximate solution of a set of real symmetric positive-definite linear equations with multiple right-hand sides,  , where  has been factorized by f03aec (nag_real_cholesky).
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Error Indicators and Warnings
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"NE_INT_ARG_LT"
On entry, n must not be less than 1:  .
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Accuracy
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The accuracy of the computed solutions depends on the conditioning of the original matrix. For a detailed error analysis see page 39 of Wilkinson and Reinsch (1971).
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Further Comments
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The time taken by nag_real_cholesky_solve_mult_rhs (f04agc) is approximately proportional to  .
The function may be called with the same actual 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 := 4:
nrhs := 1:
tda := 4:
tdb := 1:
tdx := 1:
a := Matrix([[5, 7, 6, 5], [3.130495168499706, 10, 8, 7], [2.683281572999748, -0.8944271909999157, 10, 9], [2.23606797749979, -6.332401570587769e-16, 2.121320343559642, 10]], datatype=float[8], order='C_order'):
p := Vector([0.4472135954999579, 2.236067977499789, 0.7071067811865476, 1.414213562373092], datatype=float[8]):
b := Matrix([[23], [32], [33], [31]], datatype=float[8], order='C_order'):
x := Matrix(4, 1, datatype=float[8], order='C_order'):
NAG:-f04agc(a, p, b, x, 'n' = n, 'nrhs' = nrhs, 'tda' = tda, 'tdb' = tdb, 'tdx' = tdx):
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