240 research outputs found
New family of iterative methods with high order of convergence for solving nonlinear systems
In this paper we present and analyze a set of predictor-corrector iterative methods with increasing order of convergence, for solving systems of nonlinear equations. Our aim is to achieve high order of convergence with few Jacobian and/or functional evaluations. On the other hand, by applying the pseudocomposition technique on each proposed scheme we get to increase their order of convergence, obtaining new high-order and efficient methods. We use the classical efficiency index in order to compare the obtained schemes and make some numerical test.This research was supported by Ministerio de Ciencia y TecnologĂa MTM2011-28636-C02-02 and by FONDOCYT 2011-1-B1-33, RepĂșblica Dominicana.Cordero Barbero, A.; Torregrosa SĂĄnchez, JR.; Penkova Vassileva, M. (2013). New family of iterative methods with high order of convergence for solving nonlinear systems. En Numerical Analysis and Its Applications. Springer Verlag. 222-230. https://doi.org/10.1007/978-3-642-41515-9_23S222230Cordero, A., Hueso, J.L., MartĂnez, E., Torregrosa, J.R.: A modified Newton-Jarrattâs composition. Numer. Algor. 55, 87â99 (2010)Cordero, A., Hueso, J.L., MartĂnez, E., Torregrosa, J.R.: Efficient high-order methods based on golden ratio for nonlinear systems. Applied Mathematics and Computation 217(9), 4548â4556 (2011)Cordero, A., Torregrosa, J.R.: Variants of Newtonâs Method using fifth-order quadrature formulas. Applied Mathematics and Computation 190, 686â698 (2007)Cordero, A., Torregrosa, J.R.: On interpolation variants of Newtonâs method for functions of several variables. Journal of Computational and Applied Mathematics 234, 34â43 (2010)Cordero, A., Torregrosa, J.R., Vassileva, M.P.: Pseudocomposition: a technique to design predictor-corrector methods for systms of nonlinear equtaions. Applied Mathematics and Computation 218(23), 11496â11504 (2012)Nikkhah-Bahrami, M., Oftadeh, R.: An effective iterative method for computing real and complex roots of systems of nonlinear equations. Applied Mathematics and Computation 215, 1813â1820 (2009)Ostrowski, A.M.: Solutions of equations and systems of equations. Academic Press, New York (1966)Shin, B.-C., Darvishi, M.T., Kim, C.-H.: A comparison of the Newton-Krylov method with high order Newton-like methods to solve nonlinear systems. Applied Mathematics and Computation 217, 3190â3198 (2010
Multipoint efficient iterative methods and the dynamics of Ostrowski's method
This is an Author's Accepted Manuscript of an article published in JosĂ© L. Hueso, Eulalia MartĂnez & Carles Teruel (2019) Multipoint efficient iterative methods and the dynamics of Ostrowski's method, International Journal of Computer Mathematics, 96:9, 1687-1701, DOI: 10.1080/00207160.2015.1080354 in the International Journal of Computer Mathematics, SEP 2 2019 [copyright Taylor & Francis], available online at: http://www.tandfonline.com/10.1080/00207160.2015.1080354[EN] In this work, we introduce a modification into the technique, presented in A. Cordero, J.L. Hueso, E. Martinez, and J.R. Torregrosa [Increasing the convergence order of an iterative method for nonlinear systems, Appl. Math. Lett. 25 (2012), pp. 2369-2374], that increases by two units the convergence order of an iterative method. The main idea is to compose a given iterative method of order p with a modification of Newton's method that introduces just one evaluation of the function, obtaining a new method of order p+2, avoiding the need to compute more than one derivative, so we improve the efficiency index in the scalar case. This procedure can be repeated n times, with the same approximation to the derivative, obtaining new iterative methods of order p+2n. We perform different numerical tests that confirm the theoretical results. By applying this procedure to Newton's method one obtains the well known fourth order Ostrowski's method. We finally analyse its dynamical behaviour on second and third degree real polynomials.This research was supported by Ministerio de Economia y Competitividad under grant PGC2018-095896-B-C22 and by the project of Generalitat Valenciana Prometeo/2016/089.Hueso, JL.; MartĂnez Molada, E.; Teruel-Ferragud, C. (2019). Multipoint efficient iterative methods and the dynamics of Ostrowski's method. International Journal of Computer Mathematics. 96(9):1687-1701. https://doi.org/10.1080/00207160.2015.1080354S16871701969Amat, S., Busquier, S., & Plaza, S. (2010). Chaotic dynamics of a third-order Newton-type method. Journal of Mathematical Analysis and Applications, 366(1), 24-32. doi:10.1016/j.jmaa.2010.01.047Cordero, A., & Torregrosa, J. R. (2007). Variants of Newtonâs Method using fifth-order quadrature formulas. Applied Mathematics and Computation, 190(1), 686-698. doi:10.1016/j.amc.2007.01.062Cordero, A., MartĂnez, E., & Torregrosa, J. R. (2009). Iterative methods of order four and five for systems of nonlinear equations. Journal of Computational and Applied Mathematics, 231(2), 541-551. doi:10.1016/j.cam.2009.04.015Cordero, A., Hueso, J. L., MartĂnez, E., & Torregrosa, J. R. (2012). Increasing the convergence order of an iterative method for nonlinear systems. Applied Mathematics Letters, 25(12), 2369-2374. doi:10.1016/j.aml.2012.07.005Jarratt, P. (1966). Some fourth order multipoint iterative methods for solving equations. Mathematics of Computation, 20(95), 434-434. doi:10.1090/s0025-5718-66-99924-
alpha-particle production in the scattering of 6He by 208Pb at energies around the Coulomb barrier
New experimental data from the scattering of 6He+208Pb at energies around and
below the Coulomb barrier are presented. The yield of breakup products coming
from projectile fragmentation is dominated by a strong group of
particles.
The energy and angular distributions of this group have been analyzed and
compared with theoretical calculations. This analysis indicates that the
particles emitted at backward angles in this reaction are mainly due
to two-neutron transfer to weakly bound states of the final nucleus.Comment: 20 pages, 5 figures. Nuclear Physics A792 (2007) 2-1
Spectroscopy of Na: Bridging the two-proton radioactivity of Mg
The unbound nucleus Na, the intermediate nucleus in the two-proton
radioactivity of Mg, was studied by the measurement of the resonant
elastic scattering reaction Ne(p,Ne)p performed at 4 A.MeV.
Spectroscopic properties of the low-lying states were obtained in a R-matrix
analysis of the excitation function. Using these new results, we show that the
lifetime of the Mg radioactivity can be understood assuming a sequential
emission of two protons via low energy tails of Na resonances
An unusual cause of acute cardiogenic shock in the operating room
A 51-year-old man with a renal carcinoma with inferior vena cava (IVC) invasion was referred to our hospital for the performance of a radical nephrectomy with IVC thrombus excision. To prevent embolism, an IVC filter was implanted the day before surgery below the suprahepatic veins. On nephrectomy completion, the clinical status of the patient started to deteriorate and an unsuccessful attempt was made to excise the IVC thrombus. The patient developed profound refractory hypotension without significant bleeding and worsening splanchnic stasis was noted. A transesophageal echocardiogram was immediately performed in the operating room, revealing a hemispheric mass protruding from the IVC ostium to the right atrium, completely blocking all venous return. Volume depletion was evident by low left and right atrial volumes and increased septum mobility. No other abnormalities were found that could explain the shock, namely ventricular dysfunction or valvular disease. Cardiac surgery consultation was immediately obtained, ultimately deciding to perform a median sternotomy with direct exploration of right atrium. Under cardiopulmonary bypass, a 6-cm long thrombotic mass was identified, involving the IVC filter, blocking all lower body venous return; the removal of the mass reversed the shock. The patient had an uneventful recovery. Adverse outcomes associated with IVC filters are common. Our case highlights the importance of a team approach to rapid changes in hemodynamic status in the operating room, including the surgeon, the anesthesiologist, and the cardiologist. It also emphasizes the pivotal role of transesophageal echocardiogram in the clinical evaluation of severely unstable patien
UHECR as Decay Products of Heavy Relics? The Lifetime Problem
The essential features underlying the top-down scenarii for UHECR are
discussed, namely, the stability (or lifetime) imposed to the heavy objects
(particles) whatever they be: topological and non-topological solitons,
X-particles, cosmic defects, microscopic black-holes, fundamental strings. We
provide an unified formula for the quantum decay rate of all these objects as
well as the particle decays in the standard model. The key point in the
top-down scenarii is the necessity to adjust the lifetime of the heavy object
to the age of the universe. This ad-hoc requirement needs a very high
dimensional operator to govern its decay and/or an extremely small coupling
constant. The natural lifetimes of such heavy objects are, however, microscopic
times associated to the GUT energy scale (sim 10^{-28} sec. or shorter). It is
at this energy scale (by the end of inflation) where they could have been
abundantly formed in the early universe and it seems natural that they decayed
shortly after being formed.Comment: 11 pages, LaTex, no figures, updated versio
Two-sided Grassmann-Rayleigh quotient iteration
The two-sided Rayleigh quotient iteration proposed by Ostrowski computes a
pair of corresponding left-right eigenvectors of a matrix . We propose a
Grassmannian version of this iteration, i.e., its iterates are pairs of
-dimensional subspaces instead of one-dimensional subspaces in the classical
case. The new iteration generically converges locally cubically to the pairs of
left-right -dimensional invariant subspaces of . Moreover, Grassmannian
versions of the Rayleigh quotient iteration are given for the generalized
Hermitian eigenproblem, the Hamiltonian eigenproblem and the skew-Hamiltonian
eigenproblem.Comment: The text is identical to a manuscript that was submitted for
publication on 19 April 200
Single Spin Asymmetry in Polarized Proton-Proton Elastic Scattering at GeV
We report a high precision measurement of the transverse single spin
asymmetry at the center of mass energy GeV in elastic
proton-proton scattering by the STAR experiment at RHIC. The was measured
in the four-momentum transfer squared range \GeVcSq, the region of a significant interference between the
electromagnetic and hadronic scattering amplitudes. The measured values of
and its -dependence are consistent with a vanishing hadronic spin-flip
amplitude, thus providing strong constraints on the ratio of the single
spin-flip to the non-flip amplitudes. Since the hadronic amplitude is dominated
by the Pomeron amplitude at this , we conclude that this measurement
addresses the question about the presence of a hadronic spin flip due to the
Pomeron exchange in polarized proton-proton elastic scattering.Comment: 12 pages, 6 figure
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