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RegularisedInverse.example <- function(){
hilbert <- function(n) { i <- 1:n; 1 / outer(i - 1, i, "+")}
K_h8 <- hilbert(8);
r8 <- 1:8
alphaReg_robust<- 1e-4
Sa8_robust <- RegularisedSol(K_h8,alphaReg_robust,r8,"LF")
alphaReg_accurate<- 1e-10
Sa8_accurate <- RegularisedSol(K_h8,alphaReg_accurate,r8,"LF")
## when pre multiplied by K_h8 ,the expected solution is 1:8
## User can check the influence of the choice of alphaReg
SolRobust <- K_h8 %*% Sa8_robust
SolAccurate <- K_h8 %*% Sa8_accurate
SolSolve <- K_h8 %*% solve(K_h8,r8)
print("expected solution =1:8")
list(robust=SolRobust,accurate=SolAccurate,solve=SolSolve)
}
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