We obtain Weyl type asymptotics for the quantised derivative \dj \mkern 1muf of a function content-type="math/mathml"> f f ...

Computing the structured singular value (or ) is a bottleneck of the robustness analysis and synthesis of control systems. In this paper, it is shown that is identical to the maximum singular value for an important class of matrices called reciprocal, which re ects the intrinsic symmetry of physical world.

We have developed algorithms to count singular values of a bidiagonalmatrix which are greater than a speci ed value This requires the transformation of the singular value problem to an equivalent symmetric eigenvalue problem The counting of sin gular values is paramount in the design of bisection and multisection type algorithms for computing singular values on serial and parallel machines The ...

We consider the problem of constructing nonnegative matrices with prescribed extremal singular values. In particular, given 2n−1 real numbers σ ( j) 1 and σ ( j) j , j = 1, . . . , n, we construct an n×n nonnegative bidiagonal matrix B and an n×n nonnegative semi-bordered diagonal matrix C , such that σ ( j) 1 and σ ( j) j are, respectively, the minimal and the maximal singular values of certai...

Abstract. Let p be a prime for which the congruence group Γ0(p) ∗ is of genus zero, and j∗ p be the corresponding Hauptmodul. Let f be a nearly holomorphic modular form of weight 1/2 on Γ0(4p) which satisfies some congruence condition on its Fourier coefficients. We interpret f as a vector valued modular form. Applying Borcherds lifting of vector valued modular forms we construct infinite produ...

In this paper we investigate least squares matching problems, extending the methods of our earlier paper 1] in such a way as to make them applicable to problems involving the sets of points that are so complex that approximate answers are of interest. These problems are formulated in terms of continuous descent equations, and lower bounds on the quality of the best match are obtained in terms o...

The notion of a low rank update arises in many important applications. This paper deals with the inverse problem of updating a rectangular matrix by additive low rank matrices so as to reposition the associated singular values. The setting is analogous to the classical pole assignment problem where eigenvalues of a square matrix are relocated. Precise and easy-to-check necessary and sufficient ...