6,678 research outputs found
The Future of Canadian Climate Policy — with Marc Lee
No full textMarc Lee is a Senior Economist at the Canadian Centre for Policy Alternatives\u27 BC Office. In addition to tracking federal and provincial budgets and economic trends, Marc has published on a range of topics from poverty and inequality to globalization and international trade to public services and regulation. Marc is the Co-Director of the Climate Justice Project, a research partnership with UBC\u27s School of Community and Regional Planning that examines the links between climate change policies and social justice.Resources:Climate Justice Project: www.policyalternatives.ca/projects/cli…tice-projectMarc Lee\u27s Posts on Policy Note: www.policynote.ca/author/marclee/Canadian Centre for Policy Alternatives: www.policyalternatives.ca/Marc\u27s Twitter: twitter.com/MarcLeeCCPA International Panel on Climate Change, 2021 report: www.ipcc.ch/report/ar6/wg1
Climate Justice & Inequality: The Future of Canadian Climate Policy — with Marc Lee
No full textMarc Lee is a Senior Economist at the Canadian Centre for Policy Alternatives\u27 BC Office. In addition to tracking federal and provincial budgets and economic trends, Marc has published on a range of topics from poverty and inequality to globalization and international trade to public services and regulation. Marc is the Co-Director of the Climate Justice Project, a research partnership with UBC\u27s School of Community and Regional Planning that examines the links between climate change policies and social justice.Resources: Climate Justice Project: https://www.policyalternatives.ca/projects/climate-justice-projectMarc Lee\u27s Posts on Policy Note: https://www.policynote.ca/author/marclee/Canadian Centre for Policy Alternatives: https://www.policyalternatives.ca/Marc\u27s Twitter: https://twitter.com/MarcLeeCCPA International Panel on Climate Change, 2021 report: https://www.ipcc.ch/report/ar6/wg1
Fast and stable algorithms for reducing diagonal plus semiseparable matrices to tridiagonal and bidiagonal form
No full textBackward Error Measures for Roots of Polynomials
No full textWe analyze different measures for the backward error of a set of numerical approximations for the roots of a polynomial. We focus mainly on the element-wise mixed backward error introduced by Mastronardi and Van Dooren, and the tropical backward error introduced by Tisseur and Van Barel. We show that these measures are equivalent under suitable assumptions. We also show relations between these measures and the classical element-wise and norm-wise backward error measures.sponsorship: Sascha Timme was supported by the Deutsche Forschungsgemeinschaft (German Research Foundation) Graduiertenkolleg Facets of Complexity (GRK 2434). Marc Van Barel was partially supported by the Research Council KU Leuven, C1-project (Numerical Linear Algebra and Polynomial Computations), and by the Fund for Scientific Research Flanders (Belgium), G.0828.14N (Multivariate polynomial and rational interpolation and approximation), and EOS Project No 30468160. (Deutsche Forschungsgemeinschaft (German Research Foundation) Graduiertenkolleg Facets of Complexity|GRK 2434, Research Council KU Leuven, C1-project (Numerical Linear Algebra and Polynomial Computations), Fund for Scientific Research Flanders (Belgium)|G.0828.14N, EOS Project|30468160)status: Publishe
A new approach to the rational interpolation problem
No full textAbstractWe shall reformulate the classical Newton-Padé rational interpolation problem (NPRIP) to take away several drawbacks of the Newton-Padé approach. A new recursive algorithm, not reordering the interpolation points, will be designed, enabling us to give a parametrization of all solutions, not only for the linearized RIP but also for the proper RIP. This paper generalizes our earlier work where the Padé approximation problem, i.e., when all the interpolation points coincide at the origin, was solved by reformulating it as a minimal partial realization problem (Van Barel (1989), Van Barel and Bultheel (1989))
A new approach to the rational interpolation problem: The vector case
No full textAbstractWe generalize our earlier results on rational interpolation which were given in Van Barel and Bultheel (this journal, 1990) for the scalar case and in Bultheel and Van Barel (1990) for the vector case when all the interpolation points coincide, to the case of vector data given at arbitrary points that may coincide or not. This is the vector-valued Newton-Padé problem. We give a recursive algorithm which has the important advantage over other algorithms that we do not need a reordering of the given interpolation data to overcome a singularity in the interpolation table, not even in the nonnormal vector case. It also generates all the information needed to give all solutions of the problem
Orthogonal rational functions and diagonal-plus-semiseparable matrices
No full textThe space of all proper rational functions with prescribed real poles is considered. Given a set of points zi on the real line and the weights wi, we define the discrete inner product &lt,φ,ψ> := Σni=o wi2φ(zi)ψ(zi). In this paper we derive an efficient method to compute the coefficients of a recurrence relation generating a set of orthonormal rational basis functions with respect to the discrete inner product. We will show that these coefficients can be computed by solving an inverse eigenvalue problem for a diagonal-plus-semiseparable matrix
Optimization-based algorithms for the rank- Block Term Decomposition and related decompositions
No full textThe canonical polyadic and rank-(Lt,Lt,1) block term decomposition are two closely related tensor decompositions. We present a decomposition that generalizes both of the former and examine which algorithms are suited for its computation. Accordingly, these algorithms are also directly applicable to the CPD and rank-(Lt,Lt,1) BTD. We compare the popular alternating least squares scheme with several general unconstrained optimization techniques, as well as inexact nonlinear least squares methods. In the latter, the structure of the Jacobian's Gramian is exploited by means of efficient expressions for its matrix-vector product. Combined with an effective preconditioner -- which is in fact equivalent to an ALS step -- these methods prove to be a promising alternative for ALS, often converging to a more accurate result using significantly less floating point operations, especially for difficult problems. This is joint work with Lieven De Lathauwer (K.U.Leuven Kortrijk, Belgium) and Marc Van Barel (K.U.Leuven, Belgium).status: Publishe
UKMARC AMC: Draft Rev 4.0: UK MARC format for archives and manuscripts control (UK MARC AMC)
No full textThis draft is the first attempt to establish a UK MARC specifically for Archives and Manuscripts Control since the British Library indicated that it would countenance such extensions to the national UK MARC format. In order to keep consistency with the general UK MARC format, standard UK MARC subject fields are not included in this document, since they should be taken from the latest version of the UK MARC manual. {A note of them should perhaps be included in UK MARC AMC.} {NB Text in braces is intended to be explanatory material for readers of this draft}. Certain other fields have not been included that might occasionally be used in the cataloguing of archival materials but would generally only be used for such materials in organizations which were combining archive
databases with library databases. This MARC version is intended for use with descriptions of archive or anuscript material that follow, or fit, the traditional style of cataloguing: we assume that these will normally relate
to paper or parchment originals. It is not intended for use with descriptions of other kinds of material. For these, fields may be drawn from the appropriate UK MARC document. MARC versions for use with archives in special formats should be developed, in order to complete the full range of facilities available to archivists and curators
Solving polynomial eigenvalue problems by a scaled block companion linearization
No full textLarge Solving polynomial eigenvalue problems by a scaled block companion linearization
Marc Van Barel
The polynomial eigenvalue problem (PEP) is to look for nonzero vectors v (right eigenvectors) and corresponding eigenvalues λ such that
P(λ) v = 0, where P(z) is an s × s matrix polynomial. The standard way to solve the PEP is via linearization, the latter being a square matrix polynomial L(z) of degree one such that E(z) L(z) F(z) = matrix(P(z), 0; 0, I) with E(z) and F(z) unimodular matrix polynomials.
An abundance of linearizations have appeared in the literature based on the representation of P(z) in different bases, e.g., degree graded bases such as the monomial basis, the Chebyshev basis, ..., or interpolation bases, such as the Lagrange polynomials.
If the matrix polynomial P(z) has degree d and is given in the monomial basisis, i.e., as
P(z) = P_0+P_1z+...+P_dz^d, then L(z)= matrix(P_d, P_{d-1},...,P_1, P_0| I_s, -zI_s, 0_s,..., 0_s| ...| 0_s, 0_s, I_s, -z I_s)
is a block companion linearization of the grade d+1 matrix polynomial 0 z^{d+1} + P(z).
In this talk, we describe a two-sided diagonal scaling of L(z) based on the max-times roots of the associated max-time polynomial p(x) = max(∥P_i∥ x^i; 0 ≤ i ≤ d).
We show that this scaling when combined with a deflation of the s extra eigenvalues at infinity allows an adapted version of the QZ algorithm to compute the eigenvalues of P with small backward errors. Unlike Gaubert and Sharify's approach, which uses the max-times roots of p(x) to scale the eigenvalue parameter and require one call of the QZ algorithm per max-times root, our approach only requires one call to the QZ algorithm.
This is joint work with Francoise Tisseur.status: Publishe
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