# BuildLaguerreSystem: function BuildLaguerreSystem In LaplaceDeconv: Laplace Deconvolution with Noisy Discrete Non-Equally Spaced Observations on a Finite Time Interval

## Description

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.

## Usage

 `1` ```BuildLaguerreSystem(a, g, times, Mmax, tol = 1e-07) ```

## Arguments

 `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)

## Value

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

## Author(s)

Y. Rozenholc and M. Pensky

## Examples

 ```1 2 3 4 5 6 7 8 9``` ```## Not run: library(LaplaceDeconv) t = seq(0,10,l=50) g = exp(-5*t) # compute the elements needed for the Laplace deconvolution with kernel observations g at times t bFctLagMat = BuildLaguerreSystem(a=1/2,g,t,M=10) ## End(Not run) ```

LaplaceDeconv documentation built on May 30, 2017, 2:46 a.m.