in this note we characterize polynomial numerical hulls of matrices $a in m_n$ such that$a^2$ is hermitian. also, we consider normal matrices $a in m_n$ whose $k^{th}$ power are semidefinite. for such matriceswe show that $v^k(a)=sigma(a)$.

In this paper, the behavior of the pseudopolynomial numerical hull of a square complex matrix with respect to structured perturbations and its radius is investigated.

In this note we characterize polynomial numerical hulls of matrices $A in M_n$ such that$A^2$ is Hermitian. Also, we consider normal matrices $A in M_n$ whose $k^{th}$ power are semidefinite. For such matriceswe show that $V^k(A)=sigma(A)$.

We study the complexity of computing the mixed-integer hull conv(P ∩ Z ×R) of a polyhedron P . Given an inequality description, with one integer variable, the mixed-integer hull can have exponentially many vertices and facets in d. For n, d fixed, we give an algorithm to find the mixed integer hull in polynomial time. Given P = conv(V ) and n fixed, we compute a vertex description of the mixed-...

We display methods that allow for computations of spectra, pseudospectra and resolvents of linear operators on Hilbert spaces and also elements in unital Banach algebras. The paper considers two different approaches, namely, pseudospectral techniques and polynomial numerical hull theory. The former is used for Hilbert space operators whereas the latter can handle the general case of elements in...

Nowadays, application of high speed crafts with large tonnage is of our country's essences. In order to gain high speed, new multi hull crafts are traditional. A hull form having been used recently in frigates is the Trimaran. Trimaran hull form and motion have been extensively studied due to the development of numerical and analytical methods as well as the exploitation of experimental setup. ...

In this paper, we propose a highly e cient accelerating method for the restarted Arnoldi iteration to compute the eigenvalues of a large nonsymmetric matrix. Its e ectiveness is proved by various numerical experiments and comparisons with other approaches. Several new results on the characteristics of the polynomial acceleration are also reported. The Arnoldi iteration has been the most popular...

This paper presents a new algorithm for the convex hull problem, which is based on a reduction to a combinatorial decision problem CompletenessC, which in turn can be solved by a simplicial homology computation. Like other convex hull algorithms, our algorithm is polynomial (in the size of input plus output) for simplicial or simple input. We show that the “no”-case of CompletenessC has a certi...

When solving a linear algebraic system Ax = b with GMRES, the relative residual norm at each step is bounded from above by the so-called ideal GMRES approximation. This worstcase bound is sharp (i.e. it is attainable by the relative GMRES residual norm) in case of a normal matrix A, but it need not characterize the worst-case GMRES behavior if A is nonnormal. Characterizing the tightness of thi...