Description Usage Arguments Value Author(s) Examples
build the matrix associated to the Laguerre function basis at given times, its QR decomposition, the coefficients of the kernel function of the Laplace convolution and the Toeplitz matrix associated to the Laplace convolution with the kernel g.
1 | BuildLaguerreSystem(a, g, times, Mmax, tol = 1e-07)
|
a, |
numeric, the scale parameter of the Laguerre functions basis |
g, |
numeric vector, the observed values of the known Laplace convolution kernel at the observation times |
times, |
numeric vector, the observation times |
Mmax, |
numeric, the maximal degree |
tol, |
tolerance in qr decomposition (default 1e-7) |
a list containing:
gcoef
, numeric vector, the coefficients of g in the Laguerre functions basis
GM
, numeric matrix, the Toeplitz matrix of the Laplace convolution with g
Phi
, numeric matrix, the Laguerre function basis
Phi.qr
, the QR decomposition of Phi
Mmax
, numeric, the maximal degree
a
, numeric, the scale of the Laguerre function basis
g
, numeric vector, the kernel
times
, numeric vector, the observation times
Y. Rozenholc and M. Pensky
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