NAG Library Function Document
nag_ode_bvp_ps_lin_coeffs (d02uac) obtains the Chebyshev coefficients of a function discretized on Chebyshev Gauss–Lobatto points. The set of discretization points on which the function is evaluated is usually obtained by a previous call to nag_ode_bvp_ps_lin_cgl_grid (d02ucc)
||nag_ode_bvp_ps_lin_coeffs (Integer n,
const double f,
nag_ode_bvp_ps_lin_coeffs (d02uac) computes the coefficients
, of the interpolating Chebyshev series
which interpolates the function
evaluated at the Chebyshev Gauss–Lobatto points
denotes the Chebyshev polynomial of the first kind of degree
. In terms of your original variable,
say, the input values at which the function values are to be provided are
are respectively the upper and lower ends of the range of
over which the function is required.
Canuto C (1988) Spectral Methods in Fluid Dynamics 502 Springer
Canuto C, Hussaini M Y, Quarteroni A and Zang T A (2006) Spectral Methods: Fundamentals in Single Domains Springer
Trefethen L N (2000) Spectral Methods in MATLAB SIAM
n – IntegerInput
On entry: , where the number of grid points is . This is also the largest order of Chebyshev polynomial in the Chebyshev series to be computed.
f – const doubleInput
On entry: the function values
, for .
c – doubleOutput
On exit: the Chebyshev coefficients,
, for .
fail – NagError *Input/Output
The NAG error argument (see Section 3.6
in the Essential Introduction).
6 Error Indicators and Warnings
Dynamic memory allocation failed.
On entry, argument had an illegal value.
On entry, .
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG
The Chebyshev coefficients computed should be accurate to within a small multiple of machine precision.
8 Parallelism and Performance
nag_ode_bvp_ps_lin_coeffs (d02uac) is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
nag_ode_bvp_ps_lin_coeffs (d02uac) makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the Users' Note
for your implementation for any additional implementation-specific information.
The number of operations is of the order and the memory requirements are ; thus the computation remains efficient and practical for very fine discretizations (very large values of ).
See Section 10
in nag_ode_bvp_ps_lin_solve (d02uec).