Roots of bivariate polynomial systems via determinantal representations

We give two determinantal representations for a bivariate polynomial. They may be used to compute the zeros of a system of two of these polynomials via the eigenvalues of a two-parameter eigenvalue problem. The first determinantal representation is suitable for polynomials with scalar or matrix coefficients, and consists of matrices with asymptotic order $n^2/4$, where $n$ is the degree of the polynomial. The second representation is useful for scalar polynomials and has asymptotic order $n^2/6$. The resulting method to compute the roots of a system of two bivariate polynomials is competitive with some existing methods for polynomials up to degree 10, as well as for polynomials with a small number of terms.Comment: 22 pages, 9 figure

Polynomial two-parameter eigenvalue problems and matrix pencil methods for stability of delay-differential equations

Several recent methods used to analyze asymptotic stability of delay-differential equations (DDEs) involve determining the eigenvalues of a matrix, a matrix pencil or a matrix polynomial constructed by Kronecker products. Despite some similarities between the different types of these so-called matrix pencil methods, the general ideas used as well as the proofs differ considerably. Moreover, the available theory hardly reveals the relations between the different methods. In this work, a different derivation of various matrix pencil methods is presented using a unifying framework of a new type of eigenvalue problem: the polynomial two-parameter eigenvalue problem, of which the quadratic two-parameter eigenvalue problem is a special case. This framework makes it possible to establish relations between various seemingly different methods and provides further insight in the theory of matrix pencil methods. We also recognize a few new matrix pencil variants to determine DDE stability. Finally, the recognition of the new types of eigenvalue problem opens a door to efficient computation of DDE stability

Scaling data streams with Catmandu and linked data fragments

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Fractional regularization matrices for linear discrete ill-posed problems

The numerical solution of linear discrete ill-posed problems typically requires regularization. Two of the most popular regularization methods are due to Tikhonov and Lavrentiev. These methods require the choice of a regularization matrix. Common choices include the identity matrix and finite difference approximations of a derivative operator. It is the purpose of the present paper to explore the use of fractional powers of the matrices {Mathematical expression} (for Tikhonov regularization) and A (for Lavrentiev regularization) as regularization matrices, where A is the matrix that defines the linear discrete ill-posed problem. Both small- and large-scale problems are considered. © 2013 Springer Science+Business Media Dordrecht

Balancing Accumulation and Affordability: How Dutch Housing Politics Moved from Private-Rental Liberalization to Regulation

This paper answers the question why the Dutch state has gone from vigorously stimulating private-rental growth and liberalization to actively restricting the tenure. Answering this question is important in understanding an emergent wave of more restrictive, or even “post-neoliberal” housing policies across countries. This paper presents an analysis of the changing private-rental politics in the period following the Great Financial Crisis, combined with a quantitative study of renters’ housing outcomes. The central argument is that policies promoting private-rental growth and liberalization and the subsequent turn restrictive policies are both outcomes of the state seeking to balance the property-led accumulation with middle-class residential demands. Supportive policies were the result of a presumed alignment of the interests of capital, the state and the middle classes, but ongoing liberalization has undermined middle-class housing affordability – revealing a key tension between capital and middle-class interests. This tension triggered new, more restrictive policies