1,197 research outputs found
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 , where is the degree
of the polynomial. The second representation is useful for scalar polynomials
and has asymptotic order . 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
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
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