1A New Block Algorithm for Full-Rank Solution of the Sylvester-observer Equation.

AbstractA new block algorithm for computing a full rank so-lution of the Sylvester-observer equation arising in state estima-tion is proposed. The major Computational Kernels of this algo-rithm are (i) solutions of ordinary Sylvester equations, in which case each one of the matrices is of much smaller order than that of the system matrix and furthermore, this small matrix can be chosen arbitrarily, (ii) orthogonal reduction of small order matri-ces. There are numerically stable algorithms for performing these tasks. The algorithm is rich in Level 3 Basic Linear Algebra Sub-programs (BLAS-3) computations and thus suitable for high per-formance computing. Furthermore, the results on numerical ex-periments on some benchmark examples show that the algorithm has better accuracy than that of some of the existing block algo-rithms for this problem