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....

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.

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).

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.