<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0120-419X</journal-id>
<journal-title><![CDATA[Revista Integración]]></journal-title>
<abbrev-journal-title><![CDATA[Integración - UIS]]></abbrev-journal-title>
<issn>0120-419X</issn>
<publisher>
<publisher-name><![CDATA[Universidad Industrial de Santander]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0120-419X2018000200117</article-id>
<article-id pub-id-type="doi">10.18273/revint.v36n2-2018004</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Un algoritmo tipo Newton globalizado para resolver la ecuación cuadrática matricial]]></article-title>
<article-title xml:lang="en"><![CDATA[A globalized Newton type algorithm to solve the matrix quadratic equation]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Macías]]></surname>
<given-names><![CDATA[Mauricio]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Martínez]]></surname>
<given-names><![CDATA[Héctor J.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Pérez]]></surname>
<given-names><![CDATA[Rosana]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad del Cauca Departamento de Matemáticas ]]></institution>
<addr-line><![CDATA[Popayán ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad del Valle Departamento de Matemáticas ]]></institution>
<addr-line><![CDATA[Cali ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2018</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2018</year>
</pub-date>
<volume>36</volume>
<numero>2</numero>
<fpage>117</fpage>
<lpage>132</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0120-419X2018000200117&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0120-419X2018000200117&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0120-419X2018000200117&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen En este artículo se presenta una globalización del algoritmo cuasi-Newton local propuesto en [16] para resolver la ecuación cuadrática matricial. Se demuestra que la estrategia de globalización usada no interfiere en la tasa de convergencia del algoritmo cuasi-Newton. Pruebas numéricas muestran un buen desempeño del algoritmo global propuesto. MSC2010: 15A24, 39B42, 49M15, 65H20, 90C53.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract In this paper we propose a globalized quasi-Newton algorithm to solve the quadratic matrix equation. It is shown that the globalization strategy used does not interfere in the convergence of the local quasi-Newton algorithm. We present some numerical tests that show the good performance of the global quasi-Newton algorithm.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Función matricial]]></kwd>
<kwd lng="es"><![CDATA[método de Newton]]></kwd>
<kwd lng="es"><![CDATA[ecuaciones matriciales no lineales]]></kwd>
<kwd lng="es"><![CDATA[convergencia]]></kwd>
<kwd lng="en"><![CDATA[Matrix function]]></kwd>
<kwd lng="en"><![CDATA[secant method]]></kwd>
<kwd lng="en"><![CDATA[nonlinear matrix equations]]></kwd>
<kwd lng="en"><![CDATA[su-perlinear convergence]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<label>[1]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[ermúdez]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Durán]]></surname>
<given-names><![CDATA[R.G.]]></given-names>
</name>
<name>
<surname><![CDATA[Rodríguez]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Salomin]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Finite element analysis of a quadratic eingenvalue problem arising in dissipative acoustics]]></article-title>
<source><![CDATA[SIAM J. Numer. Anal]]></source>
<year>2000</year>
<volume>38</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>267-91</page-range></nlm-citation>
</ref>
<ref id="B2">
<label>[2]</label><nlm-citation citation-type="confpro">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Clark]]></surname>
<given-names><![CDATA[J.V.]]></given-names>
</name>
<name>
<surname><![CDATA[Zhou]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
<name>
<surname><![CDATA[Pister]]></surname>
<given-names><![CDATA[K.S.J]]></given-names>
</name>
</person-group>
<source><![CDATA[Nodal simulation for MEMS design using SUGAR v0.5]]></source>
<year>1988</year>
<conf-name><![CDATA[ International Conference on Modeling and Simulation of Microsystems, Semiconductors, Sensors and Actuators]]></conf-name>
<conf-loc>Santa Clara, CA </conf-loc>
<page-range>308-13</page-range></nlm-citation>
</ref>
<ref id="B3">
<label>[3]</label><nlm-citation citation-type="confpro">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Clark]]></surname>
<given-names><![CDATA[J.V.]]></given-names>
</name>
<name>
<surname><![CDATA[Zhou]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
<name>
<surname><![CDATA[Pister]]></surname>
<given-names><![CDATA[K.S.J]]></given-names>
</name>
</person-group>
<source><![CDATA[Modified nodal analysis for MEMS with multi-energydomains]]></source>
<year>2000</year>
<conf-name><![CDATA[ International Conference on Modeling and Simulation of Microsystems, Semiconductors, Sensors and Actuators]]></conf-name>
<conf-loc>San Diego, CA </conf-loc>
</nlm-citation>
</ref>
<ref id="B4">
<label>[4]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Davila]]></surname>
<given-names><![CDATA[C.E]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A subspace approach to estimation of autoregressive parameters from noisy measurements]]></article-title>
<source><![CDATA[IEEE Trans. Signal Process]]></source>
<year>1988</year>
<volume>46</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>531-4</page-range></nlm-citation>
</ref>
<ref id="B5">
<label>[5]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Davis]]></surname>
<given-names><![CDATA[J.G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Numerical solution of a quadratic matrix equation]]></article-title>
<source><![CDATA[SIAM J. Sci. Statict. Comput]]></source>
<year>1981</year>
<volume>2</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>164-75</page-range></nlm-citation>
</ref>
<ref id="B6">
<label>[6]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dennis]]></surname>
<given-names><![CDATA[J.E.]]></given-names>
</name>
<name>
<surname><![CDATA[Schnabel]]></surname>
<given-names><![CDATA[R.B]]></given-names>
</name>
</person-group>
<source><![CDATA[Numerical methods for unconstrained optimization and nonlinear equations]]></source>
<year>1996</year>
<publisher-loc><![CDATA[Philadephia ]]></publisher-loc>
<publisher-name><![CDATA[SIAM]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B7">
<label>[7]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Golub]]></surname>
<given-names><![CDATA[H.G.]]></given-names>
</name>
<name>
<surname><![CDATA[Van Loan]]></surname>
<given-names><![CDATA[C.F]]></given-names>
</name>
</person-group>
<source><![CDATA[Matrix Computations]]></source>
<year>1996</year>
<publisher-loc><![CDATA[Baltimore, MD ]]></publisher-loc>
<publisher-name><![CDATA[The Jonhs Hopkins University Press, Jonhs Hopskins University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B8">
<label>[8]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Higham]]></surname>
<given-names><![CDATA[N.J]]></given-names>
</name>
</person-group>
<source><![CDATA[Functions of matrices theory and computations]]></source>
<year>2008</year>
<publisher-loc><![CDATA[Philadephia, PA ]]></publisher-loc>
<publisher-name><![CDATA[SIAM]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B9">
<label>[9]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Higham]]></surname>
<given-names><![CDATA[N.J.]]></given-names>
</name>
<name>
<surname><![CDATA[Kim]]></surname>
<given-names><![CDATA[H]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Numerical analysis of a quadratic matrix equation]]></article-title>
<source><![CDATA[IMA J. Numer. Anal]]></source>
<year>2000</year>
<volume>20</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>499-519</page-range></nlm-citation>
</ref>
<ref id="B10">
<label>[10]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Higham]]></surname>
<given-names><![CDATA[N.J.]]></given-names>
</name>
<name>
<surname><![CDATA[Kim]]></surname>
<given-names><![CDATA[H]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Solving a quadratic matrix equation by Newton's methods with exact line searches]]></article-title>
<source><![CDATA[SIAM J. Anal. Appl]]></source>
<year>2001</year>
<volume>23</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>303-16</page-range></nlm-citation>
</ref>
<ref id="B11">
<label>[11]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kay]]></surname>
<given-names><![CDATA[S.M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Noise compensation for autoregressive spectral estimates]]></article-title>
<source><![CDATA[IEEE Trans. Acoust. Speech Signal Process]]></source>
<year>1980</year>
<volume>28</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>292-303</page-range></nlm-citation>
</ref>
<ref id="B12">
<label>[12]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kim]]></surname>
<given-names><![CDATA[H.M]]></given-names>
</name>
</person-group>
<source><![CDATA[Numerical methods for solving a quadratic matix equation]]></source>
<year>2000</year>
<page-range>59-60</page-range><publisher-name><![CDATA[Manchester University]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B13">
<label>[13]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lancaster]]></surname>
<given-names><![CDATA[P]]></given-names>
</name>
</person-group>
<source><![CDATA[Lambda-Matrices and Vibrating Systems]]></source>
<year>1966</year>
<publisher-loc><![CDATA[Oxford-New York-Paris ]]></publisher-loc>
<publisher-name><![CDATA[Pergamon Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B14">
<label>[14]</label><nlm-citation citation-type="confpro">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Laub]]></surname>
<given-names><![CDATA[A.J]]></given-names>
</name>
</person-group>
<source><![CDATA[Efficient multivariable frequency response computations]]></source>
<year>1980</year>
<conf-name><![CDATA[ 19IEEE Conference on Decision and Control including the Symposium on Adaptive Processes]]></conf-name>
<conf-loc>Albuquerque, USA </conf-loc>
<page-range>39-41</page-range></nlm-citation>
</ref>
<ref id="B15">
<label>[15]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Long]]></surname>
<given-names><![CDATA[J.H.]]></given-names>
</name>
<name>
<surname><![CDATA[Zhang]]></surname>
<given-names><![CDATA[L]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Improved Newton's method with exact line searches to solve quadratic matrix equation]]></article-title>
<source><![CDATA[J. Comput. Appl. Math]]></source>
<year>2008</year>
<volume>222</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>645-54</page-range></nlm-citation>
</ref>
<ref id="B16">
<label>[16]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Macías]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Martínez]]></surname>
<given-names><![CDATA[H.J.]]></given-names>
</name>
<name>
<surname><![CDATA[Pérez]]></surname>
<given-names><![CDATA[R]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Un algoritmo cuasi-Newton para resolver la ecuación cuadrática matricial]]></article-title>
<source><![CDATA[Rev. Integr. Temas Mat]]></source>
<year>2016</year>
<volume>34</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>187-206</page-range></nlm-citation>
</ref>
<ref id="B17">
<label>[17]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Macías]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Martínez]]></surname>
<given-names><![CDATA[H.J.]]></given-names>
</name>
<name>
<surname><![CDATA[Pérez]]></surname>
<given-names><![CDATA[R]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Sobre la convergencia de un método secante para ecuaciones matriciales no lineales]]></article-title>
<source><![CDATA[Rev. Integr. Temas Mat]]></source>
<year>2014</year>
<volume>32</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>181-97</page-range></nlm-citation>
</ref>
<ref id="B18">
<label>[18]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Monsalve]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Raydan]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Newton's method and secant methods: A long-standing relationship from vectors to matrices]]></article-title>
<source><![CDATA[Port. Math]]></source>
<year>2011</year>
<volume>68</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>431-75</page-range></nlm-citation>
</ref>
<ref id="B19">
<label>[19]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Monsalve]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Raydan]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A secant method for nonlinear matrix problems]]></article-title>
<source><![CDATA[Numerical linear algebra in signals, systems and control]]></source>
<year>2011</year>
<volume>80</volume>
<page-range>387-402</page-range><publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B20">
<label>[20]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Nocedal]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Wright]]></surname>
<given-names><![CDATA[J.G]]></given-names>
</name>
</person-group>
<source><![CDATA[Numerical Optimizations]]></source>
<year>1999</year>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[Springer-Verlag]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B21">
<label>[21]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Reddy]]></surname>
<given-names><![CDATA[S.C.]]></given-names>
</name>
<name>
<surname><![CDATA[Schmid]]></surname>
<given-names><![CDATA[P.J.]]></given-names>
</name>
<name>
<surname><![CDATA[Henningson]]></surname>
<given-names><![CDATA[D.S]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Pseudospectra of the Orr-Sommerfeld operator]]></article-title>
<source><![CDATA[SIAM J. App. Math]]></source>
<year>1993</year>
<volume>53</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>15-47</page-range></nlm-citation>
</ref>
<ref id="B22">
<label>[22]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Smith]]></surname>
<given-names><![CDATA[H.A.]]></given-names>
</name>
<name>
<surname><![CDATA[Singh]]></surname>
<given-names><![CDATA[R.K.]]></given-names>
</name>
<name>
<surname><![CDATA[Sorensen]]></surname>
<given-names><![CDATA[D.C]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Formulation and solution of the nonlinear, damped eigenvalue problem for skeletal systems]]></article-title>
<source><![CDATA[Internat. J. Numer. Methods Engrg]]></source>
<year>1995</year>
<volume>38</volume>
<numero>18</numero>
<issue>18</issue>
<page-range>3071-85</page-range></nlm-citation>
</ref>
<ref id="B23">
<label>[23]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tisseur]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Meerbergen]]></surname>
<given-names><![CDATA[K]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The quadratic eigenvalue problem]]></article-title>
<source><![CDATA[SIAM Rev]]></source>
<year>2001</year>
<volume>43</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>235-86</page-range></nlm-citation>
</ref>
<ref id="B24">
<label>[24]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tisseur]]></surname>
<given-names><![CDATA[F]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Backward error and condition of polynomial eigenvalue problems]]></article-title>
<source><![CDATA[Linear Algebra Appl]]></source>
<year>2000</year>
<volume>309</volume>
<numero>1-3</numero>
<issue>1-3</issue>
<page-range>339-61</page-range></nlm-citation>
</ref>
<ref id="B25">
<label>[25]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Thomson]]></surname>
<given-names><![CDATA[W.T]]></given-names>
</name>
</person-group>
<source><![CDATA[Teoría de vibraciones con aplicaciones]]></source>
<year>1996</year>
<publisher-name><![CDATA[CRC Press]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
