This paper considers the problem of quadratic mean-square stabilization of a class of stochastic linear systems using quantized state feedback. Different from the previous works where the system is restricted to be deterministic, we focus on stochastic systems with multiplicative noises in both the system matrix and the control input. A static quantizer is used in the feedback channel. It is sh...

It was recently shown that the alternating direction method with logarithmicquadratic proximal regularization can yield an efficient algorithm for a class of variational inequalities with separable structures. This paper further shows the O(1/t) convergence rate for this kind of algorithms. Both the cases with a simple or general Glowinski’s relaxation factor are discussed.

A new unified method for designing both paraunitary cosine-modulated FIR filter banks and cosine-modulated wavelets is proposed in this paper. This problem has been formulated as a quadratic-constrained least-squares (QCLS) minimization problem in which all constraint matrices are symmetric and positive definite. Furthermore, a specific analog neural network whose energy function is chosen as t...

Our purpose is to deal with quadratic operators acting between vector lattices of continuous mappings on a compact Hausdorff space. In our first main result we characterize quadratic-multiplicative operators, whereas in the second one we provide necessary and sufficient conditions for a quadratic operator to be proportional to the square of a continuous linear operator.

The MM principle is a device for creating optimization algorithms satisfying the ascent or descent property. The current survey emphasizes the role of the MM principle in nonlinear programming. For smooth functions, one can construct an adaptive interior point method based on scaled Bregman barriers. This algorithm does not follow the central path. For convex programming subject to nonsmooth co...

in this paper, a fundamentally new method, based on the denition, is introduced for numerical computation of eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices. some examples are provided to show the accuracy and reliability of the proposed method. it is shown that the proposed method gives other sequences than that of existing methods but they still are convergent to t...

in this paper, we solve a linear system of second-order boundary value problems by using the quadratic b-spline nite el- ement method (fem). the performance of the method is tested on one model problem. comparisons are made with both the analyti- cal solution and some recent results.the obtained numerical results show that the method is ecient.

As a generalization of the famous four square theorem of Lagrange, Ramanujan found all positive definite integral quaternary diagonal quadratic forms that represent all positive integers. In this paper, we find all positive definite integral quinary diagonal quadratic forms that represent all positive definite integral binary quadratic forms. §

in this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-archimedean number with $alpha^{-2}neq 3$. using the fixed point method and the direct method, we prove the hyers-ulam stability of the quadratic $alpha$-functional equation (0.1) in non-archimedean banach spaces.

This paper presents a method for designing linear, quadratic and cubic interpolators that compute elementary functions using truncated multipliers, squarers and cubers. Initial coefficient values are obtained using a Chebyshev series approximation. A direct search algorithm is then used to optimize the quantized coefficient values to meet a user-specified error constraint. The algorithm minimiz...