Hi, My name is Raj and I am Phd student in Computer Graphics. I am interested in tackling the problem of uBLAS Matrix Solver and in order to write my proposal, I am looking for inputs for which of the following algorithms will be most useful for prospective users in boost-numeric library. Here is a categorical list of all the prospective ones which will bring uBLAS updated to other commercial libraries like Eigen/Armadillo. Please let me know your preferences.... *David Bellot* : As a potential mentor, do you have any specific additions or deletions for this list? This could also be useful for other candidates pursuing this project. *DENSE SOLVERS AND DECOMPOSITION* : 1) *QR Decomposition* - *(Must have)* For orthogonalization of column spaces and solutions to linear systems. (Bonus : Also rank revealing..) 2) *Cholesky Decomposition* - *(Must have)* For symmetric Positive Definite systems often encountered in PDE for FEM Systems... 3) *Householder Method* - Conversion to tridiagonal form for eigen solvers. *SPARSE SOLVERS AND PRECONDITIONERS* : 1) *Conjugate Gradient* - *(Must have)* For symmetric Positive Definite systems, this is the kryvlov space method of choice. Both general and preconditioned variants need to be implemented for convergence issues. 2) *BiCGSTAB* *(Needs introspection)* - For non symmetric systems.. 3) *Incomplete Cholesky Decomposition* *(Good to have)* - For symmetric Positive definite sparse matrices, to be used as preconditioner as extension to (1) for preconditioned CG Methods ... 4) *Jacobi Preconditioner* *(Must have)* - As prerequisite for step(1). *EIGEN DECOMPOSITION MODULES (ONLY FOR DENSE MODULES)**:* 1) *Symmetric Eigen Values* - *(Must have)* Like SSYEV Module in Lapack - That is first reduction to a tridiagonal form using Householder then using QR Algorithm for Eigen Value computation. 2) *NonSymmetric Eigen Values* - *(Good to have)* Like SGEEV module in Lapack - using Schur decompositions as an intermediate step in the above algorithm. 3) *Generalized Eigen Values* - *(needs introspection)* I use this in my research a lot and its a good thing to have.. ** Computing Eigen Decomposition of sparse modules needs special robust numerical treatment using implicitly restarted arnoldi iterations and may be treated as optional extensions.