Su m á r i o : 1. Introdução; 2. A importância de informações sobre custos para a melhoria da qualidade do gasto público; 3. Motivações e objetivos para a adoção de regimes contábeis que gerem informações sobre os custos do governo; 4. A adoção da contabilidade de competência deve levar necessariamente à adoção também de um orçamento de competência?; 5. O debate atual: da informação à decisão; 6. A experiência internacional e as diretrizes para adoção de um sistema de custos no setor público brasileiro; 7. Síntese e conclusões.Su m m a ry : 1. Introduction; 2. The importance of cost information for the improvement of public expenditure; 3. Motives and goals of accounting regimes that manage government expenditure information; 4. The adoption of accrual accounting must necessarily also lead to accrual budgeting?; 5. The current debate: from information to decision; 6. International experience and the guidelines for the adoption of a costing system in the Brazilian public sector; 7. Summary and conclusions.

Some fast algorithms for computing the eigenvalues of a (block) companion matrix have recently appeared in the literature. In this paper we generalize the approach to encompass unitary plus low rank matrices of the form A = U + XY H where U is a general unitary matrix. Three important cases for applications are U unitary diagonal, U unitary block Hessenberg and U unitary in block CMV form. Our extension exploits the properties of a larger matrix obtained by a certain embedding of the Hessenberg reduction of A suitable to maintain its structural properties. We show that can be factored as product of lower and upper unitary Hessenberg matrices possibly perturbed in the first k rows, and, moreover, such a data-sparse representation is well suited for the design of fast eigensolvers based on the QR iteration. The resulting algorithm is fast and backward stable.We first recall some basic properties of unitary matrices which play an important role in the derivation of our methods.Lemma 1 Let U be a unitary matrix of size n. Then rank (U (α, β)) = rank (U (J\α, J\β)) + |α| + |β| − n where J = {1, 2, . . . , n} and α and β are subsets of J. If α = {1, . . . , h} and β = J\α, then we have rank (U (1 : h, h+1 : n)) = rank (U (h+1 : n, 1 : h)), for all h = 1, . . . , n−1.

Abstract.In this paper we present a novel matrix method for polynomial rootfinding. By exploiting the properties of the QR eigenvalue algorithm applied to a suitable CMV-like form of a companion matrix we design a fast and computationally simple structured QR iteration.

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