An iterative approach for joint optimization of a scalar error-feedback matrix and a coordinate transformation matrix is developed to minimize the roundoff noise subject to the l2-norm dynamic-range scaling constraints. When the iterative algorithm converges and the optimal coordinate transformation matrix is obtained, the diagonal error-feedback matrix is derived to minimize the noise gain in ...

For a noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the joint rank-k numerical range associated with the error operators of the channel is non-empty. In this paper, geometric properties of the joint rank k-numerical range are obtained and their implications to quantum computing are discussed. It is shown that for a given k if the dimension of the un...

this paper addresses adaptive observer design problem for joint estimation of the states and unknown parameters for a class of nonlinear systems which satisfying one-sided lipschitz and quadratic inner bounded conditions. it’s shown that the stability of the proposed observer is related to finding solutions to a quadratic inequality consists of state and parameter errors. a coordinate transform...

in this note, a generalization of higher rank numerical range isintroduced and some of its properties are investigated