The approximation of y=Ay + B't)y +c(t) by linear multistep methods is studied. It is supposed that the matrix A is real symmetric and negative semidefinite, that the multistep method has an interval of absolute stability [—s, 0], and that h2 II A II < s where h is the time step. A priori error bounds are derived which show that the exponential multiplication factor is of the formexp{r;i||B|||„...

It is shown that for every 1 ≤ s ≤ n, the probability that the s-th largest eigenvalue of a random symmetric n-by-n matrix with independent random entries of absolute value at most 1 deviates from its median by more than t is at most 4e−t 2/32s2 . The main ingredient in the proof is Talagrand’s Inequality for concentration of measure in product spaces.

Let Sn be the positive real symmetric matrix of order n with (i, j ) entry equal to ( i + j − 2 j − 1 ) , and let x be a positive real number. Eigenvalues of the Hadamard (or entry wise) power S n are considered. In particular for k a positive integer, it is shown that both the Perron root and the trace of S n are approximately equal to 4 4k−1 ( 2n− 2 n− 1 )k . © 2005 Elsevier Inc. All rights r...

In  cite{GL}, B. Gerla and I. Leuc{s}tean introduced the notion of similarity on MV-algebra. A similarity MV-algebra is an MV-algebra endowed with a binary operation $S$ that verifies certain additional properties. Also, Chirtec{s} in cite{C}, study the notion of similarity on L ukasiewicz-Moisil algebras. In particular, strong similarity L ukasiewicz-Moisil algebras were defined. In this paper...

Introduced the notion of symmetric circulant matrix on skew field, an easy method is given to determine the inverse of symmetric circulant matrix on skew field , with this method , we derived the formula of determine inverse about several special type of symmetric circulant matrix. Mathematics Subject Classification: 05A19, 15A15

Motivated by the problem of learning a linear regression model whose parameter is a large fixed-rank non-symmetric matrix, we consider the optimization of a smooth cost function defined on the set of fixed-rank matrices. We adopt the geometric framework of optimization on Riemannian quotient manifolds. We study the underlying geometries of several well-known fixed-rank matrix factorizations and...

A b s t r a c t. The unbiased estimator of risk of the orthogonally invariant es-timator of the skew-symmetric normal mean matrix is obtained, and a class of minimax estimators and their order-preserving modification are proposed. The estimators have applications in paired comparisons model. A Monte Carlo study to compare the risks of the estimators is given.

We show that the correlation functions associated to symmetrized increasing subsequence problems can be expressed as pfaffians of certain antisymmetric matrix kernels, thus generalizing the result of [11] for the unsymmetrized case. Introduction In [11], Okounkov derived the following symmetric function identity: For any finite subset S ⊂ Z,

A positive de…nite symmetric matrix quali…es as a quantum mechanical covariance matrix if and only if + 12 i~ 0 where is the standard symplectic matrix. This well-known condition is a strong version of the uncertainty principle, which can be reinterpreted in terms of the topological notion of symplectic capacity, closely related to Gromov’s non-squeezing theorem. We show that a recent re…nement...

Our main goal in this paper is to investigate stochastic ternary antiderivatives (STAD). First, we will introduce the random antiderivative operator. Then, by introducing aggregation function using special functions such as Mittag-Leffler (MLF), Wright (WF), H-Fox (HFF), Gauss hypergeometric (GHF), and exponential (EXP-F), select optimal control performing necessary calculations. Next, consider...