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README.md

@@ -1,4 +1,5 @@
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 # hippylibx
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@@ -34,4 +35,4 @@ hIPPYlibx provides a robust implementation of the inexact Newton-conjugate gradi
 
 In hIPPYlibx, the posterior covariance is approximated by the inverse of the Hessian of the negative log posterior evaluated at the MAP point. This Gaussian approximation is exact when the parameter-to-observable map is linear; otherwise, its logarithm agrees to two derivatives with the log posterior at the MAP point, and thus it can serve as a proposal for Hessian-based Markov chain Monte Carlo (MCMC) methods. hIPPYlibx makes the construction of the posterior covariance tractable by invoking a low-rank approximation of the Hessian of the log likelihood.
 
-hIPPYlibx also offers scalable methods for sample generation. To sample large scale spatially correlated Gaussian random fields from the prior distribution, hIPPYlibx implements a method that strongly relies on the structure of the covariance operator defined as the inverse of a differential operator: by exploiting the assembly procedure of finite element matrices hIPPYlibx constructs a sparse Cholesky-like rectangular decomposition of the precision operator. To sample from a local Gaussian approximation to the posterior (such as at the MAP point) hIPPYlibx exploits the low rank factorization of the Hessian of the log likelihood to correct samples from the prior distribution.
+hIPPYlibx also offers scalable methods for sample generation. To sample large scale spatially correlated Gaussian random fields from the prior distribution, hIPPYlibx implements a method that strongly relies on the structure of the covariance operator defined as the inverse of a differential operator: by exploiting the assembly procedure of finite element matrices hIPPYlibx constructs a sparse Cholesky-like rectangular decomposition of the precision operator. To sample from a local Gaussian approximation to the posterior (such as at the MAP point) hIPPYlibx exploits the low rank factorization of the Hessian of the log likelihood to correct samples from the prior distribution.