We develop a general theory of almost Hadamard matrices. These are by definition the matrices H ∈ MN (R) having the property that U = H/ √ N is orthogonal, and is a local maximum of the 1-norm on O(N). Our study includes a detailed discussion of the circulant case (Hij = γj−i) and of the two-entry case (Hij ∈ {x, y}), with the construction of several families of examples, and some 1-norm comput...

H,-norm of the approximation error for both methods satisfies 16, 91 In this paper we propose an efficient computational a p rn proach to minimize the H,-norm of a transfer-function OT+I 5 /IG(s) G,(s)/Im 1 2 x ai (2) matrix depending affinely on a set of free parame.=?+I ters. The minimization problem, formulated as a semiinfinite convex programming problem, is solved via a where > . . . > 0, ...

In this paper we discuss the problem of computing the H∞-norms of transfer functions associated to large-scale descriptor systems. We exploit the relationship between the H∞-norm and the structured complex stability radius of the corresponding system pencil. To compute the structured stability radius we consider so-called structured pseudospectra. Namely, we have to find the pseudospectrum that...

Anderson acceleration (AA) is a technique for accelerating the convergence of fixed-point iterations. In this paper, we apply AA to sequence functions and modify norm in its internal optimization problem H−s norm, some positive integer s, bias it towards low-frequency spectral content residual. We analyze by quantifying improvement over Picard iteration. find that based on H−2 well-suited solve...

In this contribution, we first introduce the concept of metrical T-norm-based similarity measure for hesitant fuzzy sets (HFSs) {by using the concept of T-norm-based distance measure}. Then,the relationship of the proposed {metrical T-norm-based} similarity {measures} with the {other kind of information measure, called the metrical T-norm-based} entropy measure {is} discussed. The main feature ...

Approximation Result. Consider an abstract symmetric and continuous bilinear form a(·, ·) : V × V 7→ IR, as well as a collection of linear functionals {fl}l=1 ⊂ V ′, where V ⊂ H and H is a Hilbert space with norm ‖ · ‖. We make the following assumptions on a(·, ·), V , H, ‖ · ‖ and {fl}: A1. a(·, ·) is positive semi-definite and defines a semi-norm | · |a on V , i.e. |v|a = a(v, v) ≥ 0, for all...

An L1 norm minimization scheme is applied to the determination of the impulse response vector h of flaws detected in practical examples of ultrasonic nondestructive evaluation in CANDU nuclear reactors. For each problem, parametric programming is applied to find the optimum value of the damping parameter that will yield the best estimate of h according to a quantified performance factor. This p...