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On Sound Compilation of Reals

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Polar Codes: Robustness of the Successive Cancellation Decoder with Respect to Quantization

Rüdiger Urbanke, Seyed Hamed Hassani

Polar codes provably achieve the capacity of a wide array of channels under successive decoding. This assumes infinite precision arithmetic. Given the successive nature of the decoding algorithm, one might worry about the sensitivity of the performance to ...

Ieee2012

Trustworthy Numerical Computation in Scala

Viktor Kuncak, Eva Darulova

Modern computing has adopted the floating point type as a default way to describe computations with real numbers. Thanks to dedicated hardware support, such computations are efficient on modern architectures. However, rigorous reasoning about the resulting ...

2011

On Rigorous Numerical Computation as a Scala Library

Viktor Kuncak, Eva Darulova

Modern programming languages have adopted the floating point type as a way to describe computations with real numbers. Thanks to the hardware support, such computations are efficient on modern architectures. However, rigorous reasoning about the resulting ...

2010

Modeling and Flatness of Rigid and Flexible Cable Suspended Underactuated Robots

Philippe Müllhaupt, Basile Graf

A modeling framework is proposed for the control of rigid and flexible cable-like systems such as cranes, together with a systematic algorithm for computing flat outputs of mechanical systems for which the flat output is a linear combi- nation of free coor ...

IEEE2010

Optimising Boltzmann codes for the PLANCK era

Julien Lesgourgues, Jan Hamann

High precision measurements of the Cosmic Microwave Background (CMB) anisotropies, as can be expected from the PLANCK satellite, will require high-accuracy theoretical predictions as well. One possible source of theoretical uncertainty is the numerical err ...

2009

Krylov subspace methods for linear systems with tensor product structure

Daniel Kressner, Christine Tobler

The numerical solution of linear systems with certain tensor product structures is considered. Such structures arise, for example, from the finite element discretization of a linear PDE on a d-dimensional hypercube. Linear systems with tensor product struc ...

Society for Industrial and Applied Mathematics2009

Bit Precision Analysis for Compressed Sensing

Mohammad Amin Shokrollahi, Mahdi Cheraghchi Bashi Astaneh

This paper studies the stability of some reconstruction algorithms for compressed sensing in terms of the bit precision. Considering the fact that practical digital systems deal with discretized signals, we motivate the importance of the total number of ac ...

2009

Splitting methods based on algebraic factorization for fluid-structure interaction

Alfio Quarteroni, Annalisa Quaini

We discuss in this paper the numerical approximation of fluid-structure interaction (FSI) problems dealing with strong added-mass effect. We propose new semi-implicit algorithms based on inexact block-LU factorization of the linear system obtained after th ...

2008

An exact solution for ideal dam-break floods on steep slopes

Christophe Ancey, Martin Rentschler

Dam-break floods on steep slopes occur in diverse settings. They may result from failure of either natural or man-made dams, and they have been responsible for the loss of thousands of lives [Costa, 1988]. Recent disasters resulting from dam-break floods o ...

American Geophysical Union2008

Numerical Mathematics

Alfio Quarteroni

Numerical mathematics is the branch of mathematics that proposes, develops, analyzes and applies methods from scientific computing to several fields including analysis, linear algebra, geometry, approximation theory, functional equations, optimization and ...

Springer2007