Publications related to Methods of computing square roots

A Householder-Based Algorithm For Hessenberg-Triangular Reduction

The QZ algorithm for computing eigenvalues and eigenvectors of a matrix pencil A - lambda B requires that the matrices first be reduced to Hessenberg-triangular (HT) form. The current method of choice for HT reduction relies entirely on Givens rotations re ...

SIAM PUBLICATIONS2018

MATHICSE Technical Report : An algebraic least squares reduced basis method for the solution of parametrized Stokes equations

Alfio Quarteroni, Simone Deparis, Andrea Manzoni, Niccolò Dal Santo

In this paper we propose a new, purely algebraic, Petrov-Galerkin reduced basis (RB) method to solve the parametrized Stokes equations, where parameters serve to identify the (variable) domain geometry. Our method is obtained as an algebraic least squares ...

MATHICSE2018

Rayleigh-Based Distributed Optical Fiber Sensing Using Least Mean Square Similarity

Luc Thévenaz, Zhisheng Yang, Li Zhang, Flavien Gyger

Large frequency shift errors induced by cross-correlation are investigated in Rayleigh-based distributed sensing. A least mean square method is proposed to reduce those errors, thus increasing the reliability and extending the measurand range. ...

Optical Society of America2018

MATHICSE Technical Report : Hierarchical B-spline Complexes of Discrete Differential Forms

Rafael Vazquez Hernandez

In this paper, we introduce the hierarchical B-spline complex of discrete differential forms for arbitrary spatial dimension. This complex may be applied to the adaptive isogeometric solution of problems arising in fluid mechanics. We derive a sufficient a ...

MATHICSE2017

MATHICSE Technical Report : Optimal explicit stabilized integrator of weak order one for stiff and ergodic stochastic differential equations

Assyr Abdulle, Gilles Vilmart

A new explicit stabilized scheme of weak order one for stiff and ergodic stochastic differential equations (SDEs) is introduced. In the absence of noise, the new method coincides with the classical deterministic stabilized scheme (or Chebyshev method) for ...

MATHICSE2017

MATHICSE Technical Report : Optimal explicit stabilized integrator of weak order one for stiff and ergodic stochastic differential equations

Assyr Abdulle, Gilles Vilmart

A new explicit stabilized scheme of weak order one for stiff and ergodic stochastic differential equations (SDEs) is introduced. In the absence of noise, the new method coincides with the classical deterministic stabilized scheme (or Chebyshev method) for ...

MATHICSE2017

On Short Sums Of Trace Functions

Philippe Michel, Chandra Sekhar Raju

We consider sums of oscillating functions on intervals in cyclic groups of size close to the square root of the size of the group. We first prove non-trivial estimates for intervals of length slightly larger than this square root (bridging the "Polya-Vinog ...

Annales Inst Fourier2017

Complexity of reversible circuits and their quantum implementations

Mathias Soeken, Nabila Abdessaied

We provide an extensive overview of upper bounds on the number of gates needed in reversible and quantum circuits. As reversible gate libraries we consider single-target gates, mixed-polarity multiple-controlled Toffoli gates, and the set consisting of the ...

2016

Near/Sub-Threshold Circuits and Approximate Computing: The Perfect Combination for Ultra-Low-Power Systems

Christian Enz, Vincent Frédéric Camus, Jérémy Lucien Maurice Schlachter

While sub/near-threshold design offers the minimal power and energy consumption, such approach strongly deteriorates circuit performances and robustness against PVT (process/voltage/temperature) variations, leading to gigantic speed penalties and large sil ...

IEEE2015

Upper bounds for the reach-avoid probability via robust optimization

Maryam Kamgarpour, John Lygeros, Tyler Summers

We consider finite horizon reach-avoid problems for discrete time stochastic systems. Our goal is to construct upper bound functions for the reach-avoid probability by means of tractable convex optimization problems. We achieve this by restricting attentio ...

2015

Methods of computing square roots

A Householder-Based Algorithm For Hessenberg-Triangular Reduction

MATHICSE Technical Report : An algebraic least squares reduced basis method for the solution of parametrized Stokes equations

Rayleigh-Based Distributed Optical Fiber Sensing Using Least Mean Square Similarity

MATHICSE Technical Report : Hierarchical B-spline Complexes of Discrete Differential Forms

MATHICSE Technical Report : Optimal explicit stabilized integrator of weak order one for stiff and ergodic stochastic differential equations

MATHICSE Technical Report : Optimal explicit stabilized integrator of weak order one for stiff and ergodic stochastic differential equations

On Short Sums Of Trace Functions

Complexity of reversible circuits and their quantum implementations

Near/Sub-Threshold Circuits and Approximate Computing: The Perfect Combination for Ultra-Low-Power Systems

Upper bounds for the reach-avoid probability via robust optimization

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MATHICSE Technical Report : Hierarchical B-spline Complexes of Discrete Differential Forms

Rayleigh-Based Distributed Optical Fiber Sensing Using Least Mean Square Similarity

A Householder-Based Algorithm For Hessenberg-Triangular Reduction

MATHICSE Technical Report : An algebraic least squares reduced basis method for the solution of parametrized Stokes equations

MATHICSE Technical Report : Optimal explicit stabilized integrator of weak order one for stiff and ergodic stochastic differential equations

MATHICSE Technical Report : Optimal explicit stabilized integrator of weak order one for stiff and ergodic stochastic differential equations

On Short Sums Of Trace Functions

Complexity of reversible circuits and their quantum implementations

Near/Sub-Threshold Circuits and Approximate Computing: The Perfect Combination for Ultra-Low-Power Systems

Upper bounds for the reach-avoid probability via robust optimization