Interval arithmetic

Formal sciences
Mathematics
Analysis
Numerical analysis

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New numerical methods for the design of efficient nonlinear plasmonic sources of light and nanosensors

Olivier Martin, Gabriel David Bernasconi, Jérémy Butet, Kuang-Yu Yang

During the last decade, important attention has been devoted to the observation of nonlinear optical processes in plasmonic nanosystems, giving rise to a new field of research called nonlinear plasmonics. The cornerstone of nonlinear plasmonics is the use ...

Spie-Int Soc Optical Engineering2016

Method and apparatus for low complexity spectral analysis of bio-signals

David Atienza Alonso, Andreas Peter Burg, Srinivasan Murali, Georgios Karakonstantis, Aviinaash Sankaranarayanan

A method and device for reducing the computational complexity of a processing algorithm, of a discrete signal, in particular of the spectral estimation and analysis of bio-signals, with minimum or no quality loss, which comprises steps of (a) choosing a do ...

2015

A Distributionally Robust Perspective on Uncertainty Quantification and Chance Constrained Programming

Daniel Kuhn, Grani Adiwena Hanasusanto, Wolfram Wiesemann

The objective of uncertainty quantification is to certify that a given physical, engineering or economic system satisfies multiple safety conditions with high probability. A more ambitious goal is to actively influence the system so as to guarantee and mai ...

Springer Verlag2015

Programming with Numerical Uncertainties

Eva Darulova

Numerical software, common in scientific computing or embedded systems, inevitably uses an approximation of the real arithmetic in which most algorithms are designed. In many domains, roundoff errors are not the only source of inaccuracy and measurement as ...

EPFL2014

Aggressively Truncated Taylor Series Method For Accurate Computation Of Exponentials Of Essentially Nonnegative Matrices

Meiyue Shao

Small relative perturbations to the entries of an essentially nonnegative matrix introduce small relative errors to entries of its exponential. It is thus desirable to compute the exponential with high componentwise relative accuracy. Taylor series approxi ...

Siam Publications2014

Sound Compilation of Reals

Viktor Kuncak, Eva Darulova

Writing accurate numerical software is hard because of many sources of unavoidable uncertainties, including finite numerical precision of implementations. We present a programming model where the user writes a program in a real-valued implementation and sp ...

ACM2014

A New Basic Logic Structure for Data-Path Computation

Giovanni De Micheli, Pierre-Emmanuel Julien Marc Gaillardon, Luca Gaetano Amarù

Nowadays, Field Programmable Gate Arrays (FPGA) implement arithmetic functions using specific circuits at the logic block level, such as the carry paths, or at the structure level adopting Digital Signal Processing (DSP) blocks. Nevertheless, all these app ...

2014

Synthesis of Fixed-Point Programs

Viktor Kuncak, Eva Darulova, Indranil Saha

Several problems in the implementations of control systems, signal-processing systems, and scientific computing systems reduce to compiling a polynomial expression over the reals into an imperative program using fixed-point arithmetic. Fixed-point arithmet ...

2013

Certifying Solutions for Numerical Constraints

Viktor Kuncak, Eva Darulova

A large portion of software is used for numerical computation in mathematics, physics and engineering. Among the aspects that make verification in this domain difficult is the need to quantify numerical errors, such as roundoff errors and errors due to the ...

2013

Omnidirectional Light Field Analysis and Reconstruction

Luigi Bagnato

Digital photography exists since 1975, when Steven Sasson attempted to build the first digital camera. Since then the concept of digital camera did not evolve much: an optical lens concentrates light rays onto a focal plane where a planar photosensitive ar ...

EPFL2012

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