Accurate computation of singular values and eigenvalues of symmetric matrices

We give the review of recent results in relative perturbation theory for eigenvalue and singular value problems and highly accurate algorithms which compute eigenvalues and singular values to the highest possible relative accuracy

Relative perturbation bound for invariant subspaces of Hermitian matrix

We give a bound for the perturbations of invariant subspaces of a non-singular Hermitian matrix H under relative additive perturbations of H. Such perturbations include the acse when the elements of H are known up to some relative tolerance. Our bound is, in appropriate cases, sharper that the classical bounds, and it generalizes some of the recent relative perturbation results

Usporedba glavnih značajki klasičnog i vakuumskog načina prikupljanja i odvodnje sanitarne otpadne vode na brodu za rasute terete

Dana je usporedba klasičnog i vakuumskog sustava odvodnje sanitarne otpadne vode iz nadgrađa broda za rasute terete od 52000 tdw s 25 članova posade. Sustavi se uspoređuju prema potrošnji svježe sanitarne vode, trošku za proizvodnju potrebne količine svježe vode, vrijednosti materijala i rada potrebnog za izradu sustava, energiji koja se troši za funkcioniranje sustava i troškovima održavanja. Rezultati analize pokazuju da vakuumskim sustavima odvodnje treba dati prednost pri ugradnji. Niži troškovi u eksploataciji brzo nadoknađuju veće početno ulaganje

A GPU-based hyperbolic SVD algorithm

A one-sided Jacobi hyperbolic singular value decomposition (HSVD) algorithm, using a massively parallel graphics processing unit (GPU), is developed. The algorithm also serves as the final stage of solving a symmetric indefinite eigenvalue problem. Numerical testing demonstrates the gains in speed and accuracy over sequential and MPI-parallelized variants of similar Jacobi-type HSVD algorithms. Finally, possibilities of hybrid CPU--GPU parallelism are discussed.Comment: Accepted for publication in BIT Numerical Mathematic

On spectral condition of J-Herminian operators

The spectral condition of a matrix H is the infimum of the condition numbers κ(Z) = ||Z|| ||Z -1||, taken over all Z such that Z -1HZ is diagonal. This number controls the sensitivity of the spectrum of H under perturbations. A matrix is called J-Hermitian if H* = JHJ for some J = J* = J -1. When diagonalizing J-Hermitian matrices it is natural to look at J-unitary Z, that is, those that satisfy Z*JZ = J. Our first result is: if there is such J-unitary Z, then the infimum above is taken on J-unitary Z, that is, the J unitary diagonalization is the most stable of all. For the special case when J-Hermitian matrix has definite spectrum, we give various upper bounds for the spectral condition, and show that all J-unitaries Z which diagonalize such a matrix have the same condition number. Our estimates are given in the spectral norm and the Hilbert-Schmidt norm. Our results are, in fact, formulated and proved in a general Hilbert space (under an appropriate generalization of the notion of \u27diagonalising\u27) and they are applicable even to unbounded operators. We apply our theory to the Klein-Gordon operator thus improving a previously known bound

FLOATING CRANE RESPONSE IN SEA WAVES

Many activities present in the offshore technology are affected by sea waves and their safety strongly depends on the sea state. The fundamental question in operation risk analysis is the limit sea state which enables the safe operation controlled in all phases: from the sea surface to the sea bottom. The safe limit sea state is especially important when some lifting operation is performed in sea waves. This paper presents a dynamical model of a floating crane in sea waves with a hanging load at a high altitude above sea level. The model is defined as a linearized coupled double pendulum where the usual 6 DOF of the floating crane oscillatory motions in waves are extended by additional 3 DOF of the swinging load. The numerical model of the floating crane is calibrated and tuned according to the measured model in a towing tank. The significant values of the crane boom top accelerations were estimated for the given design sea state with different vertical load positions. The problem is illustrated by the example of a floating crane consisting of a simple single pontoon with an ordinary land crane mounted on the deck. The reliability of the proposed method is evaluated on the basis of correlation between the calculated and measured data

Relative perturbation of invariant subspaces

In this paper we consider the upper bound for the sine of the greatest canonical angle between the original invariant subspace and its perturbation. We present our recent results which generalize some of the results from the relative perturbation theory of indefinite Hermitian matrices

Primjena ekonomskih mjerila vrsnoće u osnivanju broda

Za zadane vrijednosti nosivosti, brzine te omjera glavnih dimenzija i koeficijenta iskoristivosti istisnine osniva se inicijalni brod. Varirajući duljinu i omjere glavnih dimenzija inicijalnog broda osniva se flota brodova. Za sve brodove iz generirane flote izračunavaju se ekonomske značajke za različite kombinacije brzine, kamata i životnog vijeka. Tretirajući ove značajke kao ekonomska mjerila vrsnoće biraju se najbolji brodovi prema: najmanjem trošku izrade, najmanjem trošku izrade po toni nosivosti, najvećem koeficijentu iskoristivosti istisnine, najmanjim životnim troškovima po toni nosivosti, najmanjoj zahtijevanoj vozarini, najvećoj dobiti po toni nosivosti, najbržem povratu kapitala i najvećoj sadašnjoj vrijednosti projekta. U radu je utvrđeno da u izboru najboljeg broda prevladavaju ekonomska mjerila u odnosu na tehničke kriterije

RAČUNOVODSTVENE METODE PROCJENE USPJEŠNOSTI TOP MANADŽMENTA

The paper provides a theoretical framework to assess the adequacy of accounting measures in the evaluation of top management performance. It has often been claimed by economists that accounting measures of profitability are inadequate measures of managerial performance. Our objective is to analyse whether accounting measures are appropriate performance measures. The key characteristics of an ideal performance measure are its congruence with the principal\u27s goal (an increase in its value should reflect increase in wealth for owners of the firm) and its noisiness (it should be noiseless to uncontrollable events). Such a measure would act as both a target for management and an assessment of its performance in terms of achieving owners\u27 goal. While a stock price is perfectly congruent measure, it is not likely to be an efficient measure for incentive purposes. The article starts by contrasting the German corporate governance structure to the UK - USA one in order to find out the likely development of the Slovene corporate governance model by considering economic and legal circumstances in which the Slovene companies operate. Thereafter consideration is given to some of the empirical studies to examine the congruence of accounting profit and stock price. We then briefly overview the most widely used profitability ratios as well as additional accounting and non accounting information which help assess different aspects of top management performance. Since corporations in the touristic sector face similar problems regarding management control, the conclusions of the paper are as well applicable to the larger companies of the sector. The paper concludes with a discussion of the implications for further accounting research of this field.Rad se bavi teorijskim postavkama procjene adekvatnosti računovodstvenih metoda za vrednovanje rada top menadžmenta. Vrlo često ekonomisti tvrde da je računovodstveno mjerenje profitabilnosti neadekvatno za vrednovanje rada top menadžmenta. Stoga je naš cilj analizirati u kojoj su mjeri one zaista adekvatne. Ključna karakteristika ocjene idealnog načina mjerenja profitabilnosti je njena usklađenost s temeljnim ciljem poduzeća a mjeri se porastom bogatstva vlasnika. Takva metoda predstavlja cilj menadžmenta, a istovremeno osigurava procjenu njegova rada. Dok je cijena dionica realno mjerilo uspjeha istovremeno se ne može prihvatiti kao učinkovito sredstvo za poticajne ciljeve. U radu se komparira struktura menadžmenta korporacija u Njemačkoj s istima u Velikoj Britaniji i SAD-u, u cilju kreiranja modela razvoja slovenskog korporacijskog menadžmenta vodeći računa o ekonomskim i pravnim uvjetima u kojima ono djeluje. Nakon toga se razmatraju neka empirijska istraživanja koja proučavaju kongruenciju računovodstvenog profita i cijene dionica. Analiziraju se najčešći pokazatelji profitabilnosti kao i drugi pokazatelji koji se koriste za vrednovanje rada top menadžmenta. Kako se korporacije iz turističkog sektora susreću sa sličnim problemima u svezi kontrole menadžmenta, zaključak se rada može također primijeniti na brojna poduzeća tog sektora. Rad završava s diskusijom o implikacijama za daljnje računovodstveno istraživanje na tom području