Finite free convolutions of polynomials

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Publications associées (27)

Strictly Real Fundamental Theorem Of Algebra Using Polynomial Interlacing

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Without resorting to complex numbers or any advanced topological arguments, we show that any real polynomial of degree greater than two always has a real quadratic polynomial factor, which is equivalent to the fundamental theorem of algebra. The proof uses ...

CAMBRIDGE UNIV PRESS2021

On Randomized Trace Estimates for Indefinite Matrices with an Application to Determinants

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Randomized trace estimation is a popular and well-studied technique that approximates the trace of a large-scale matrix B by computing the average of x(T) Bx for many samples of a random vector X. Often, B is symmetric positive definite (SPD) but a number ...

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ON WAVEFRONT ABERRATIONS IN ASYMMETRIC AND MULTIPLE APERTURE OPTICAL SYSTEMS

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The present work deals with monochromatic wavefront aberrations in optical systems without symmetries. The treatment begins with a class of systems characterized by misaligned spherical surfaces whose behavior is analyzed using the wavefront aberration exp ...

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Learning in Volatile Environments With the Bayes Factor Surprise

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Surprise-based learning allows agents to rapidly adapt to nonstationary stochastic environments characterized by sudden changes. We show that exact Bayesian inference in a hierarchical model gives rise to a surprise-modulated trade-off between forgetting o ...

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Generalization Error Bounds Via Rényi-, f-Divergences and Maximal Leakage

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In this work, the probability of an event under some joint distribution is bounded by measuring it with the product of the marginals instead (which is typically easier to analyze) together with a measure of the dependence between the two random variables. ...

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Progressive Correspondence Pruning by Consensus Learning

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Correspondence pruning aims to correctly remove false matches (outliers) from an initial set of putative correspondences. The pruning process is challenging since putative matches are typically extremely unbalanced, largely dominated by outliers, and the r ...

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Feedback and Common Information: Bounds and Capacity for Gaussian Networks

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Network information theory studies the communication of information in a network and considers its fundamental limits. Motivating from the extensive presence of the networks in the daily life, the thesis studies the fundamental limits of particular network ...

EPFL2021

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