Publications related to MATHICSE Technical Report: Interpolatory rational model order reduction of parametric problems lacking uniform inf-sup stability

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We present a sampling theory for a class of binary images with finite rate of innovation (FRI). Every image in our model is the restriction of

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Multivariate Markov-type and Nikolskii-type inequalities for polynomials associated with downward closed multi-index sets

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Elsevier2015

MATHICSE Technical Report : Discrete least squares polynomial approximation with random evaluations – application to parametric and stochastic elliptic PDES

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Motivated by the numerical treatment of parametric and stochastic PDEs, we analyze the least-squares method for polynomial approximation of multivariate func- tions based on random sampling according to a given probability measure. Recent work has shown th ...

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STOCHASTIC PROCESSES AND CONSTRUCTION OF BROWNIAN MOTION

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The polynomial Hirsch conjecture states that the vertex-edge diameter of a d-dimensional polyhedron with n facets is bounded by a polynomial in d and n. For the special case where the polyhedron is defined as the set of points satisfying a system Ax ≤ b of ...

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Generalized reduced basis methods and n-width estimates for the approximation of the solution manifold of parametric PDEs

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MATHICSE Technical Report : Analysis of the discrete $L^2$ projection on polynomial spaces with random evaluations

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We analyse the problem of approximating a multivariate function by discrete least-squares projection on a polynomial space starting from random, noise-free observations. An area of possible application of such technique is Uncertainty Quantification (UQ) f ...

MATHICSE2011

MATHICSE Technical Report: Interpolatory rational model order reduction of parametric problems lacking uniform inf-sup stability

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Sampling and Reconstruction of Shapes with Algebraic Boundaries

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

Estimation in Functional Lagged Regression

Multivariate Markov-type and Nikolskii-type inequalities for polynomials associated with downward closed multi-index sets

MATHICSE Technical Report : Discrete least squares polynomial approximation with random evaluations – application to parametric and stochastic elliptic PDES

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

STOCHASTIC PROCESSES AND CONSTRUCTION OF BROWNIAN MOTION

New Results in the Theory of Linear and Integer Programming

Generalized reduced basis methods and n-width estimates for the approximation of the solution manifold of parametric PDEs

MATHICSE Technical Report : Analysis of the discrete $L^2$ projection on polynomial spaces with random evaluations

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

New Results in the Theory of Linear and Integer Programming

Estimation in Functional Lagged Regression

MATHICSE Technical Report : Analysis of the discrete $L^2$ projection on polynomial spaces with random evaluations

Multivariate Markov-type and Nikolskii-type inequalities for polynomials associated with downward closed multi-index sets

Sampling and Reconstruction of Shapes with Algebraic Boundaries

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

MATHICSE Technical Report : Discrete least squares polynomial approximation with random evaluations – application to parametric and stochastic elliptic PDES

STOCHASTIC PROCESSES AND CONSTRUCTION OF BROWNIAN MOTION

Generalized reduced basis methods and n-width estimates for the approximation of the solution manifold of parametric PDEs