Publications related to Analytic function

Functional Tucker Approximation Using Chebyshev Interpolation

Daniel Kressner, Christoph Max Strössner

This work is concerned with approximating a trivariate function defined on a tensor-product domain via function evaluations. Combining tensorized Chebyshev interpolation with a Tucker decomposition of low multilinear rank yields function approximations tha ...

SIAM PUBLICATIONS2021

On the asymptotic behavior of the solutions to parabolic variational inequalities

Maria Colombo

We consider various versions of the obstacle and thin-obstacle problems, we interpret them as variational inequalities, with non-smooth constraint, and prove that they satisfy a new constrained Lojasiewicz inequality. The difficulty lies in the fact that, ...

2020

Thermal CFTs in momentum space

Andrea Manenti

We study some aspects of conformal field theories at finite temperature in momentum space. We provide a formula for the Fourier transform of a thermal conformal block and study its analytic properties. In particular we show that the Fourier transform vanis ...

SPRINGER2020

Loops in AdS: from the spectral representation to position space

Din Carmi

We compute a family of scalar loop diagrams in AdS. We use the spectral representation to derive various bulk vertex/propagator identities, and these identities enable to reduce certain loop bubble diagrams to lower loop diagrams, and often to tree- level ...

2020

On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

Daniel Kressner, Stefano Massei, Alice Cortinovis

The problem of finding a k x k submatrix of maximum volume of a matrix A is of interest in a variety of applications. For example, it yields a quasi-best low-rank approximation constructed from the rows and columns of A. We show that such a submatrix can a ...

ELSEVIER SCIENCE INC2020

The index of singular zeros of harmonic mappings of anti-analytic degree one

Robert Gerhard Jérôme Luce

We study harmonic mappings of the form , where h is an analytic function. In particular, we are interested in the index (a generalized multiplicity) of the zeros of such functions. Outside the critical set of f, where the Jacobian of f is non-vanishing, it ...

TAYLOR & FRANCIS LTD2019

Log Barriers for Safe Non-convex Black-box Optimization

Maryam Kamgarpour, Andreas Krause, Ilnura Usmanova

We address the problem of minimizing a smooth function f0(x) over a compact set D defined by smooth functional constraints fi(x)≤0, i=1,…,m given noisy value measurements of fi(x). This problem arises in safety-critical applications, where certain paramete ...

2019

Optimal Spline Generators for Derivative Sampling

Michaël Unser, Shayan Aziznejad, Alireza Naderi

The goal of derivative sampling is to reconstruct a signal from the samples of the function and of its first-order derivative. In this paper, we consider this problem over a shift-invariant reconstruction subspace generated by two compact-support functions ...

IEEE2019

Optimization Notes

Sepand Kashani

While optimization is well studied for real-valued functions

f : \mathbb{R}^{N} \to \mathbb{R}

, many physical problems are (partially) specified in terms of complex-valued functions

f_{c} : \mathbb{C}^{N} \to \mathbb{C}^{M}

. Current optimization packag ...

2019

Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

Nicolas Henri Bernard Flammarion

We consider minimizing a nonconvex, smooth function

f

on a Riemannian manifold

\mathcal{M}

. We show that a perturbed version of Riemannian gradient descent algorithm converges to a second-order stationary point (and hence is able to escape saddle point ...

2019

Analytic function

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Functional Tucker Approximation Using Chebyshev Interpolation

On the asymptotic behavior of the solutions to parabolic variational inequalities

Thermal CFTs in momentum space

Loops in AdS: from the spectral representation to position space

On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

The index of singular zeros of harmonic mappings of anti-analytic degree one

Log Barriers for Safe Non-convex Black-box Optimization

Optimal Spline Generators for Derivative Sampling

Optimization Notes

Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

Functional Tucker Approximation Using Chebyshev Interpolation

Loops in AdS: from the spectral representation to position space

Thermal CFTs in momentum space

On the asymptotic behavior of the solutions to parabolic variational inequalities

On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

The index of singular zeros of harmonic mappings of anti-analytic degree one

Log Barriers for Safe Non-convex Black-box Optimization

Optimal Spline Generators for Derivative Sampling

Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

Optimization Notes