We provide a simple convergence analysis unified for TR and a new ARC algorithms, which we name ARCq and which is very close in spirit to trust region methods, closer than the original ARC is. We prove global convergence to second order points. We also obtain as a corollary the convergence of the original ARC method. Since one of our aims is to achieve a simple presentation, we sacrifice some g...

Stability and change in the mean levels and sources of variation in personality was examined. A sample of 149 monozygotic and 202 dizygotic twin pairs over 80 years were studied three times with a 2-year interval between measurement occasions. The Eysenck Personality Inventory to measure extraversion and neuroticism was used. Linear mixed models and Cholesky variance decomposition were carried ...

We consider the smallest eigenvalue problem for symmetric or Hermitian matrices by properties of semidefinite matrices. The work is based on a floating-point Cholesky decomposition and takes into account all possible computational and rounding errors. A computational test is given to verify that a given symmetric or Hermitian matrix is not positive semidefinite, so it has at least one negative ...

In this paper, He’s variational iteration method (VIM) has been used to obtain solutions of the seventh-order Sawada-Kotera equation (sSK) and a Lax’s seventh order KdV equations(LsKdV).The numerical solutions are compared with the Adomian decomposition method(ADM) and the known analytical solutions.The work confirms the power of the VIM in reducing the size of calculations w.r.t. ADM. Some ill...

We present a new Adaptive Regularization by Cubics (ARC) algorithm, which we name ARCq and which is very close in spirit to trust region methods, closer than the original ARC is. We prove global convergence to second-order critical points. We also obtain as a corollary the convergence of the original ARC method. We prove the optimal complexity property for the ARCq and identify the key elements...

will be uncorrelated, since 〈ĉĉ〉 − 〈ĉ〉〈ĉ〉 = I. 〈ĉ〉 = Mc, so the new window function matrix will be M. However, whereas the window functions of the original power estimates (the rows of F) are always well-behaved (they are always non-negative, and are generally quite narrow, as shown in the top panel of Figure 1), there is no guarantee that the same will hold for the new window functions. As was...

On the level-1 Fock space modules of the algebra Uq(ŝln) we define a level-0 action U0 of the Uq(ŝln), and an action of an abelian algebra of conserved Hamiltonians commuting with the U0. An irreducible decomposition of the Fock space with respect to the level-0 action is derived by constructing a base of the Fock space in terms of the Non-symmetric Macdonald Polynomials. e-mail: takemura@kurim...

The simplest way to describe the dependence for a set of financial assets is their correlation matrix. This correlation matrix can be improper when it is specified element-wise. We describe a new method for obtaining a positive definite correlation matrix starting from an improper one. The expert’s opinion and trust on each pairwise correlation is described by a beta distribution. Then, by comb...

In a wide range of practical problems correlation matrices are formed in such a way that, while symmetry and a unit diagonal are assured, they may lack semidefiniteness. We derive a variety of new upper bounds for the distance from an arbitrary symmetric matrix to the nearest correlation matrix. The bounds are of two main classes: those based on the eigensystem and those based on a modified Cho...