Factorization Method for Boundary Value Problems by Invariant Embedding presents a new theory for linear elliptic boundary value problems. The authors provide a transformation of the problem in two initial value problems that are uncoupled, enabling you to solve these successively. This method appears similar to the Gauss block factorization of the matrix, obtained in finite dimension after discretization of the problem. This proposed method is comparable to the computation of optimal feedbacks for linear quadratic control problems.- Develops the invariant embedding technique for boundary value problems- Makes a link between control theory, boundary value problems and the Gauss factorization- Presents a new theory for successively solving linear elliptic boundary value problems- Includes a transformation in two initial value problems that are uncoupled