A fast algorithm for joint eigenvalue decomposition of real matrices

We introduce an original algorithm to perform the joint eigen value decomposition of a set of real matrices. The proposed algorithm is iterative but does not resort to any sweeping procedure such as classical Jacobi approaches. Instead we use a first order approximation of the inverse of the matrix of eigen vectors and at each iteration the whole matrix of eigenvectors is updated. This algorithm is called Joint eigenvalue Decomposition using Taylor Expansion and has been designed in order to decrease the overall numerical complexity of the procedure (which is a trade off between the number of iterations and the cost of each iteration) while keeping the same level of performances. Numerical comparisons with reference algorithms show that this goal is achieved.