1 CERFACS, 42 Avenue Gaspard Coriolis, 31057 Toulouse Cedex 1, France ([email protected]). 2 The University of Tennessee, Department of Computer Science, 1122 Volunteer Blvd., Knoxville, TN 37996-3450, USA ([email protected]). 3 Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vodárenskou věž́ı 2, CZ-182 07 Prague 8, Czech Republic ([email protected]). 4 Heinrich-Heine-...

The usual recursive summation technique is just one of several ways of computing the sum of n oating point numbers. Five summation methods and their variations are analysed here. The accuracy of the methods is compared using rounding error analysis and numerical experiments. Four of the methods are shown to be special cases of a general class of methods, and an error analysis is given for this ...

We consider the smallest eigenvalue problem for symmetric or Hermitian matrices by properties of semidefinite matrices. The work is based on a floating-point Cholesky decomposition and takes into account all possible computational and rounding errors. A computational test is given to verify that a given symmetric or Hermitian matrix is not positive semidefinite, so it has at least one negative ...

In PETS 2015, Kiayias, Leonardos, Lipmaa, Pavlyk, and Tang proposed the first (n, 1)CPIR protocol with rate 1− o(1). They use advanced techniques from multivariable calculus (like the Newton-Puiseux algorithm) to establish optimal rate among a large family of different CPIR protocols. It is only natural to ask whether one can achieve similar rate but with a much simpler analysis. We propose par...

This paper derives lower bounds on the L2-norms of digital resampling filters with zero-valued input samples. This emanates from uniform-grid sampling but where some of the samples are missing. One application is found in timeinterleaved analog-to-digital converters with missing samples due to calibration at certain time instances. The square of the L2-norms correspond to scaling of the round-o...

Based on a simple mathematical property, a simple method is proposed for detecting the number of folds n contained in a given rotationaly symmetric shape. Skills to overcome the difficulty caused by sampling and rounding errors are also discussed. Experimental results are included to show the feasibility of this new method. As for shape orientation, it is just a by-product of the proposed metho...

In this paper, a combined form of the Laplace transform method with the homotopy perturbation method is proposed to solve nonlinear equations. This method is called the homotopy perturbation transform method (HPTM). The nonlinear terms can be easily handled by the use of He’s polynomials. The proposed scheme finds the solution without any discretization or restrictive assumptions and avoids the...

figures of twentieth century mathematics. He was the quintessential pure mathematician, wanting only to prove the existence of mathematical objects. And yet... And yet... There is today a great deal of work modifying his arguments to produce efficient algorithms which sort a billion items, round off a million numbers check for primality (critical for internet shopping!) and much more. We explor...

The area A inside a simple closed curve C can be estimated graphically by drawing a square lattice of sides 1/M. The number of lattice points inside C is approximately AM. If C has continuous non-zero radius of curvature, then the number of lattice points is accurate to order of magnitude at most M for any a> §. We show that if the radius of curvature of C is continuously differentiate, then th...