## 11 Citations

### A Lanczos-Stieltjes method for one-dimensional ridge function approximation and integration

- Computer Science
- 2018

The key elements of the method are approximating the univariate density of the given linear combination of inputs by repeated convolutions and a Lanczos-Stieltjes method for constructing orthogonal polynomials and Gaussian quadrature.

### Iterative Polynomial Approximation Adapting to Arbitrary Probability Distribution

- Computer Science, MathematicsSIAM J. Numer. Anal.
- 2015

The paper addresses the impact of this constraint on the method, in particular analyzing the interplay between aliasing and truncation errors, depending on the type of functional to be represented, in a new moment/generalized polynomial chaos (gPC) based approximation method.

### Efficient uncertainty propagation for network multiphysics systems

- Environmental Science
- 2013

This work proposes an intrusive methodology that exploits the structure of the network coupled multiphysics system to efficiently construct a polynomial surrogate of the model output as a function of uncertain inputs, which results in substantial computational savings.

### Systems of Gaussian process models for directed chains of solvers

- Computer ScienceComputer Methods in Applied Mechanics and Engineering
- 2019

### A method for recursively generating sequential rational approximations to $\sqrt[n]{k}$

- Computer Science, Mathematics
- 2011

A simple recursion is derived that generates a sequence of fractions approximating $\sqrt[n]{k}$ with increasing accuracy, effectively proving convergence without notions from standard analysis of infinitesimals.

### Gauss–Christoffel quadrature for inverse regression: applications to computer experiments

- Mathematics, Computer ScienceStat. Comput.
- 2019

This work employs the well-known tools from numerical analysis to produce new algorithms that improve upon the Riemann sum-based numerical integration in SIR and SAVE, and shows that this approach approximates the desired integrals, and study the behavior of LSIR and LSAVE with two numerical examples.

### Gauss–Christoffel quadrature for inverse regression: applications to computer experiments

- Mathematics, Computer ScienceStatistics and Computing
- 2018

This work employs the well-known tools from numerical analysis to produce new algorithms that improve upon the Riemann sum-based numerical integration in SIR and SAVE, and shows that this approach approximates the desired integrals, and study the behavior of LSIR and LSAVE with two numerical examples.

### Comparison of adaptive uncertainty quantification approaches for shock wave-dominated flows

- Physics
- 2012

Shock wave-dominated systems are very sensitive to uncertainties in initial or boundary conditions as they often give rise to strong non-linear responses when subject to perturbations. As global…

### Gaussian Quadrature and Polynomial Approximation for One-Dimensional Ridge Functions

- Computer ScienceSIAM J. Sci. Comput.
- 2019

Many of the input-parameter-to-output-quantity-of-interest maps that arise in computational science admit a surprising low-dimensional structure, where the outputs vary primarily along a handful of...

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- MathematicsNumerische Mathematik
- 2007

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- Computer Science, MathematicsSIAM J. Matrix Anal. Appl.
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- Computer Science
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- Computer ScienceFrontiers in applied mathematics
- 1997

This paper presents a brief overview of the State of the Art Notation Review of Relevant Linear Algebra and some of the algorithms used in this review, as well as some basic ideas of Domain Decomposition Methods.