<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/00e005a5-168f-4109-be01-2837bb8b1d4a/bg1.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">www.dbeBooks.com - An Ebook Library</div><div class="c x2 y2 w2 h3"><div class="t m0 x0 h4 y3 ff2 fs1 fc1 sc0 ls0">www.TheSolutionManual.com</div></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,-77.810000,-87.930000]}'></div></div> <div id="pf2" class="pf w3 h5" data-page-no="2"><div class="pc pc2 w3 h5"><img class="bi x3 y0 w4 h6" alt="" src="https://files.passeidireto.com/00e005a5-168f-4109-be01-2837bb8b1d4a/bg2.png"><a class="l"><div class="d m1" style="border-style:none;position:absolute;left:48.000000px;bottom:508.500000px;width:142.500000px;height:36.000000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l"><div class="d m1" style="border-style:none;position:absolute;left:238.500000px;bottom:505.500000px;width:139.500000px;height:36.000000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l"><div class="d m1" style="border-style:none;position:absolute;left:424.500000px;bottom:505.500000px;width:141.000000px;height:36.000000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l"><div class="d m1" style="border-style:none;position:absolute;left:0.000000px;bottom:34.500000px;width:610.500000px;height:175.500000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l"><div class="d m1" style="border-style:none;position:absolute;left:10.500000px;bottom:595.500000px;width:594.000000px;height:150.000000px;background-color:rgba(255,255,255,0.000001);"></div></a></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x4 y4 w5 h7" alt="" src="https://files.passeidireto.com/00e005a5-168f-4109-be01-2837bb8b1d4a/bg3.png"><div class="t m0 x4 h8 y5 ff3 fs2 fc2 sc0 ls1 ws1">Te x t s<span class="_0 blank"> </span>i n</div><div class="t m0 x4 h8 y6 ff3 fs2 fc2 sc0 ls2 ws2">Computational Science</div><div class="t m0 x4 h9 y7 ff3 fs2 fc2 sc0 ls0 ws0">and Engineering<span class="_1 blank"> </span><span class="fs3 v1">2</span></div><div class="t m0 x4 ha y8 ff3 fs4 fc2 sc0 ls3">Editors</div><div class="t m0 x4 ha y9 ff3 fs4 fc2 sc0 ls4 ws3">T<span class="_2 blank"></span>imothy J. Barth</div><div class="t m0 x4 ha ya ff3 fs4 fc2 sc0 ls0 ws0">Michael Griebel</div><div class="t m0 x4 ha yb ff3 fs4 fc2 sc0 ls0 ws0">David E. K<span class="_2 blank"></span>e<span class="_2 blank"></span>yes</div><div class="t m0 x4 ha yc ff3 fs4 fc2 sc0 ls3 ws4">Risto M. Nieminen</div><div class="t m0 x4 ha yd ff3 fs4 fc2 sc0 ls3 ws5">Dirk Roose</div><div class="t m0 x4 ha ye ff3 fs4 fc2 sc0 ls0 ws0">T<span class="_3 blank"></span>amar Schlick</div><div class="c x2 y2 w2 h3"><div class="t m0 x0 h4 y3 ff2 fs1 fc1 sc0 ls0">www.TheSolutionManual.com</div></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,-77.810000,-87.930000]}'></div></div> <div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><div class="t m0 x5 hb yf ff3 fs5 fc2 sc0 ls0 ws0">Al\ufb01o Quarteroni<span class="_4 blank"> </span>Fausto Saleri</div><div class="t m0 x5 hc y10 ff3 fs6 fc2 sc0 ls0 ws0">Scienti\ufb01c Computing</div><div class="t m0 x5 hc y11 ff3 fs6 fc2 sc0 ls5 ws6">with MA<span class="_5 blank"></span>TLAB and Octa<span class="_2 blank"></span>v<span class="_3 blank"></span>e</div><div class="t m0 x5 hd y12 ff3 fs7 fc2 sc0 ls0 ws0">Second Edition</div><div class="t m0 x5 he y13 ff3 fs8 fc2 sc0 ls6 ws7">W<span class="_2 blank"></span>ith <span class="ff4 ls7 ws8">108 </span><span class="ls0 ws9">Figures and <span class="ff4 ls7 ws8">12 </span><span class="ls8 wsa">Ta b l e s</span></span></div><div class="t m0 x6 hf y14 ff5 fs9 fc2 sc0 ls0">A<span class="ls9">BC</span></div><div class="c x2 y2 w2 h3"><div class="t m0 x0 h4 y3 ff2 fs1 fc1 sc0 ls0">www.TheSolutionManual.com</div></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,-77.810000,-87.930000]}'></div></div> <div id="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x4 y15 w5 h10" alt="" src="https://files.passeidireto.com/00e005a5-168f-4109-be01-2837bb8b1d4a/bg5.png"><div class="t m0 x7 h11 y16 ff3 fsa fc2 sc0 ls12 wsb">Al\ufb01o Quarteroni</div><div class="t m0 x7 h12 y17 ff3 fsb fc2 sc0 ls0 wsc">Ecole Polytechnique Fédérale</div><div class="t m0 x7 h12 y18 ff3 fsb fc2 sc0 ls13 wsd">de Lausanne</div><div class="t m0 x7 h12 y19 ff3 fsb fc2 sc0 ls14 wse">CMCS-Modeling and Scienti\ufb01c Computing</div><div class="t m0 x7 h12 y1a ff4 fsb fc2 sc0 ls15 wsf">1015 <span class="ff3 ls0 ws10">Lausanne, Switzerland</span></div><div class="t m0 x7 h12 y1b ff3 fsb fc2 sc0 ls16">and</div><div class="t m0 x7 h12 y1c ff3 fsb fc2 sc0 ls0 ws0">MO<span class="_2 blank"></span>X-Politecnico di Milano</div><div class="t m0 x7 h12 y1d ff3 fsb fc2 sc0 ls0 wsc">Piazza Leonardo da V<span class="_2 blank"></span>inci <span class="ff4 ls15">32</span></div><div class="t m0 x7 h12 y1e ff4 fsb fc2 sc0 ls15 wsf">20133 <span class="ff3 ls0 ws10">Milano, Italy</span></div><div class="t m0 x7 h12 y1f ff3 fsb fc2 sc0 ls0 wsc">E-mail: al\ufb01o.quarteroni@ep\ufb02.ch</div><div class="t m0 x8 h11 y16 ff3 fsa fc2 sc0 ls17 ws11">Fausto Saleri</div><div class="t m0 x8 h12 y17 ff3 fsb fc2 sc0 ls0 ws0">MO<span class="_2 blank"></span>X-Politecnico di Milano</div><div class="t m0 x8 h12 y18 ff3 fsb fc2 sc0 ls0 wsc">Piazza Leonardo da V<span class="_2 blank"></span>inci <span class="ff4 ls15">32</span></div><div class="t m0 x8 h12 y19 ff4 fsb fc2 sc0 ls15 wsf">20133 <span class="ff3 ls0 ws10">Milano, Italy</span></div><div class="t m0 x8 h12 y1a ff3 fsb fc2 sc0 lsa ws12">E-mail: fausto.saleri@polimi.it</div><div class="t m0 x7 h13 y20 ff3 fsc fc2 sc0 lsb ws13">Cover \ufb01gure by Marzio Sala</div><div class="t m0 x7 h14 y21 ff3 fsd fc2 sc0 lsb ws14">Title of the Italian original edition: <span class="ff6 ws15">Introduzione al Calcolo<span class="_6 blank"> </span>Scienti\ufb01co<span class="ff3">, Springer-V<span class="_3 blank"></span>erlag Italia, Milano, <span class="ff4 ls18">2006</span><span class="ls0">,</span></span></span></div><div class="t m0 x7 h14 y22 ff3 fsd fc2 sc0 lsb ws16">ISBN <span class="ff4 ls18">88</span><span class="ls0 ws17">-<span class="ff4 ls18">470</span>-<span class="ff4 ls18">0480</span>-<span class="ff4">2</span></span></div><div class="t m0 x7 h15 y23 ff3 fse fc2 sc0 ls0 ws0">Library of Congress Control Number: <span class="ff4 ls19">2006928277</span></div><div class="t m0 x7 h15 y24 ff3 fse fc2 sc0 ls0 ws0">Mathematics Subject Classi\ufb01cation: <span class="ff4 ls19">65</span>-<span class="ff4 ls19">01</span><span class="lsc">,<span class="ff4 ls19">68</span></span>U<span class="ff4 ls19">01</span><span class="lsd">,<span class="ff4 ls19">68</span></span>N<span class="ff4 ls19">15</span></div><div class="t m0 x7 h15 y25 ff3 fse fc2 sc0 ls1a">ISBN-<span class="ff4 lse ws18">10<span class="_7 blank"> </span>3-540-32612-X </span><span class="ls1b ws19">Springer Berlin Heidelberg Ne<span class="_2 blank"></span>w Y<span class="_3 blank"></span>ork</span></div><div class="t m0 x7 h15 y26 ff3 fse fc2 sc0 ls1a">ISBN-<span class="ff4 lse ws1a">13<span class="_7 blank"> </span>978-3-540-32612-0 </span><span class="ls1b ws1b">Springer Berlin Heidelberg Ne<span class="_2 blank"></span>w Y<span class="_3 blank"></span>ork</span></div><div class="t m0 x7 h15 y27 ff3 fse fc2 sc0 ls1a">ISBN-<span class="ff4 lse ws1c">10<span class="_7 blank"> </span>3-540-44363-0 1</span><span class="ls1b ws1b">st Edition<span class="_0 blank"> </span>Springer Berlin Heidelber<span class="_2 blank"></span>g New Y<span class="_3 blank"></span>ork</span></div><div class="t m0 x7 h16 y28 ff3 fsf fc2 sc0 ls1c ws1d">This work is subject to copyright. All rights are reserv<span class="_2 blank"></span>ed, whether the whole or part of the material is</div><div class="t m0 x7 h16 y29 ff3 fsf fc2 sc0 ls1c ws1e">concerned, speci\ufb01cally the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting,</div><div class="t m0 x7 h16 y2a ff3 fsf fc2 sc0 ls0 ws1f">reproduction on micro\ufb01lm or in any other way<span class="_3 blank"></span>, and storage<span class="_6 blank"> </span>in data banks. Duplication of this publication</div><div class="t m0 x7 h16 y2b ff3 fsf fc2 sc0 ls0 ws20">or parts thereof is permitted only under the provisions of the German Copyright Law of September <span class="ff4">9</span>,</div><div class="t m0 x7 h16 y2c ff4 fsf fc2 sc0 ls11">1965<span class="ff3 ls0 ws21">, in its current version, and permission for use must alw<span class="_2 blank"></span>ays be obtained from Springer<span class="_2 blank"></span>. V<span class="_2 blank"></span>iolations are</span></div><div class="t m0 x7 h16 y2d ff3 fsf fc2 sc0 ls0 ws0">liable for prosecution under the German Copyright Law<span class="_3 blank"></span>.</div><div class="t m0 x7 h16 y2e ff3 fsf fc2 sc0 ls1c ws22">Springer is a part of Springer Science+Business Media</div><div class="t m0 x7 h16 y2f ff3 fsf fc2 sc0 ls0 ws23">springer<span class="_2 blank"></span>.com</div><div class="t m0 x6 h17 y30 ff3 fs10 fc2 sc0 ls0">c</div><div class="t m0 x7 h18 y31 ff7 fs11 fc2 sc0 lsf">\ue001<span class="ff3 fsf ls1c ws22 v2">Springer-V<span class="_3 blank"></span>erlag Berlin Heidelberg <span class="ff4 ls11">2003<span class="ff3 ls10">,</span>2006</span></span></div><div class="t m0 x7 h16 y32 ff3 fsf fc2 sc0 ls1c ws24">Printed in The Netherlands</div><div class="t m0 x7 h16 y33 ff3 fsf fc2 sc0 ls1c ws25">The use of general descriptiv<span class="_2 blank"></span>e names, registered names, trademarks, etc. in this publication does not imply<span class="_2 blank"></span>,</div><div class="t m0 x7 h16 y34 ff3 fsf fc2 sc0 ls1c ws26">ev<span class="_2 blank"></span>en in the absence of a speci\ufb01c statement, that such names are exempt from the rele<span class="_2 blank"></span>vant protecti<span class="_2 blank"></span>ve laws</div><div class="t m0 x7 h16 y35 ff3 fsf fc2 sc0 ls0 ws27">and regulations and therefore free for general use.</div><div class="t m0 x7 h16 y36 ff3 fsf fc2 sc0 ls0 ws0">T<span class="_2 blank"></span>ypesetting: by the authors and techbooks using a Springer L</div><div class="t m0 x9 h19 y37 ff3 fs12 fc2 sc0 ls0">A</div><div class="t m0 xa h16 y38 ff3 fsf fc2 sc0 ls0">T</div><div class="t m0 xb h16 y39 ff3 fsf fc2 sc0 ls0">E</div><div class="t m0 xc h16 y38 ff3 fsf fc2 sc0 ls1c ws22">X macro package</div><div class="t m0 x7 h16 y3a ff3 fsf fc2 sc0 ls1d ws28">Cover<span class="_6 blank"> </span>des i g n :<span class="_6 blank"> </span><span class="ff6 ls0 ws29">design & production </span><span class="ls1c ws22">GmbH, Heidelberg</span></div><div class="t m0 x7 h16 y3b ff3 fsf fc2 sc0 ls1c ws24">Printed on acid-free paper<span class="_8 blank"> </span>SPIN: <span class="ff4 ls11 ws2a">11678793 46</span><span class="ls0 ws2b">/techbooks <span class="ff4 ls1e">543210</span></span></div><div class="c x2 y2 w2 h3"><div class="t m0 x0 h4 y3 ff2 fs1 fc1 sc0 ls0">www.TheSolutionManual.com</div></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,-77.810000,-87.930000]}'></div></div> <div id="pf6" class="pf w0 h0" data-page-no="6"><div class="pc pc6 w0 h0"><div class="c x2 y2 w2 h3"><div class="t m0 x0 h4 y3 ff2 fs1 fc1 sc0 ls0">www.TheSolutionManual.com</div></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,-77.810000,-87.930000]}'></div></div> <div id="pf7" class="pf w0 h0" data-page-no="7"><div class="pc pc7 w0 h0"><div class="t m0 xd h1a y3c ff8 fs13 fc2 sc0 ls0 ws0">This b<span class="_2 blank"></span>o<span class="_3 blank"></span>ok is de<span class="_2 blank"></span>dic<span class="_2 blank"></span>ate<span class="_2 blank"></span>d to</div><div class="t m0 xe h1a y3d ff8 fs13 fc2 sc0 ls1f ws2c">F<span class="_3 blank"></span>ulvia, Silvia and Marzia,</div><div class="t m0 xf h1a y3e ff8 fs13 fc2 sc0 ls0 ws0">Paola, Maria and Caterina,</div><div class="t m0 x10 h1a y3f ff8 fs13 fc2 sc0 ls0 ws2d">who make our lives</div><div class="t m0 x11 h1a y40 ff8 fs13 fc2 sc0 ls0 ws0">less scienti\ufb01c<span class="_2 blank"></span>al<span class="_9 blank"> </span>ly c<span class="_2 blank"></span>ompute<span class="_3 blank"></span>d.</div><div class="c x2 y2 w2 h3"><div class="t m0 x0 h4 y3 ff2 fs1 fc1 sc0 ls0">www.TheSolutionManual.com</div></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,-77.810000,-87.930000]}'></div></div> <div id="pf8" class="pf w0 h0" data-page-no="8"><div class="pc pc8 w0 h0"><div class="c x2 y2 w2 h3"><div class="t m0 x0 h4 y3 ff2 fs1 fc1 sc0 ls0">www.TheSolutionManual.com</div></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,-77.810000,-87.930000]}'></div></div> <div id="pf9" class="pf w0 h0" data-page-no="9"><div class="pc pc9 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x5 y41 w6 h1b" alt="" src="https://files.passeidireto.com/00e005a5-168f-4109-be01-2837bb8b1d4a/bg9.png"><div class="t m0 x4 h1c y42 ff9 fs14 fc3 sc0 ls0">Preface</div><div class="t m0 x4 h1a y43 ff8 fs13 fc4 sc0 ls20 ws2e">Pr<span class="_2 blank"></span>efac<span class="_3 blank"></span>e to the First Edition</div><div class="t m0 x12 h1a y44 ffa fs13 fc4 sc0 ls24 ws2f">This<span class="_0 blank"> </span>textbo ok<span class="_0 blank"> </span>is<span class="_0 blank"> </span>an<span class="_0 blank"> </span>in<span class="_2 blank"></span>troduction<span class="_0 blank"> </span>to<span class="_0 blank"> </span>Scien<span class="_2 blank"></span>ti\ufb01c<span class="_0 blank"> </span>Computing.<span class="_a blank"> </span>W<span class="_3 blank"></span>e<span class="_a blank"> </span>will</div><div class="t m0 x4 h1a y45 ffa fs13 fc4 sc0 ls25 ws30">illustrate sev<span class="_2 blank"></span>eral numerical methods for the computer solution of cer-</div><div class="t m0 x4 h1a y46 ffa fs13 fc4 sc0 ls25 ws31">tain classes of mathematical problems that cannot b<span class="_9 blank"> </span>e faced b<span class="_2 blank"></span>y pap<span class="_9 blank"> </span>er</div><div class="t m0 x4 h1a y47 ffa fs13 fc4 sc0 ls25 ws32">and p<span class="_9 blank"> </span>encil. W<span class="_3 blank"></span>e will sho<span class="_2 blank"></span>w ho<span class="_2 blank"></span>w to compute the zeros or the integrals</div><div class="t m0 x4 h1a y48 ffa fs13 fc4 sc0 ls25 ws33">of con<span class="_2 blank"></span>tinuous functions, solv<span class="_2 blank"></span>e linear systems, appro<span class="_2 blank"></span>ximate functions by</div><div class="t m0 x4 h1a y49 ffa fs13 fc4 sc0 ls25 ws34">p<span class="_9 blank"> </span>olynomials and construct accurate appro<span class="_2 blank"></span>ximations for the solution of</div><div class="t m0 x4 h1a y4a ffa fs13 fc4 sc0 ls1f ws35">di\ufb00eren<span class="_2 blank"></span>tial equations.</div><div class="t m0 x12 h1a y4b ffa fs13 fc4 sc0 ls24 ws36">With this aim, in Chapter 1 we will illustrate the rules of the game</div><div class="t m0 x4 h1a y4c ffa fs13 fc4 sc0 ls25 ws37">that computers adopt when storing and operating with real and complex</div><div class="t m0 x4 h1a y4d ffa fs13 fc4 sc0 ls0 ws0">n<span class="_2 blank"></span>umbers, vectors and matrices.</div><div class="t m0 x12 h1a y4e ffa fs13 fc4 sc0 ls25 ws38">In order to mak<span class="_2 blank"></span>e our presentation concrete and appealing we will</div><div class="t m0 x4 h1d y4f ffa fs13 fc4 sc0 ls1f ws39">adopt the programming environmen<span class="_2 blank"></span>t <span class="ffb ls0 ws3a">MA<span class="_3 blank"></span>TLAB <span class="ffc ls21 v3">\ue001</span><span class="ffd fs15 ls22 v3">1</span><span class="ffa ls24 ws3b v0">as a faithful com-</span></span></div><div class="t m0 x4 h1a y50 ffa fs13 fc4 sc0 ls25 ws3c">panion. W<span class="_3 blank"></span>e will gradually discov<span class="_2 blank"></span>er its principal commands, statemen<span class="_2 blank"></span>ts</div><div class="t m0 x4 h1a y51 ffa fs13 fc4 sc0 ls25 ws3d">and constructs. W<span class="_3 blank"></span>e will show ho<span class="_2 blank"></span>w to execute all the algorithms that w<span class="_2 blank"></span>e</div><div class="t m0 x4 h1a y52 ffa fs13 fc4 sc0 ls25 ws3e">in<span class="_2 blank"></span>tro<span class="_9 blank"> </span>duce throughout the b<span class="_9 blank"> </span>ook. This will enable us to furnish an im-</div><div class="t m0 x4 h1a y53 ffa fs13 fc4 sc0 ls25 ws3f">mediate quan<span class="_2 blank"></span>titative assessmen<span class="_2 blank"></span>t of their theoretical properties such as</div><div class="t m0 x4 h1a y54 ffa fs13 fc4 sc0 ls25 ws40">stabilit<span class="_2 blank"></span>y<span class="_3 blank"></span>, accuracy and complexity<span class="_3 blank"></span>. W<span class="_3 blank"></span>e will solv<span class="_2 blank"></span>e several problems that</div><div class="t m0 x4 h1a y55 ffa fs13 fc4 sc0 ls1f ws41">will b<span class="_9 blank"> </span>e raised through exercises and examples, often stemming from spe-</div><div class="t m0 x4 h1a y56 ffa fs13 fc4 sc0 ls25 ws42">ci\ufb01c applications.</div><div class="t m0 x12 h1a y57 ffa fs13 fc4 sc0 ls1f ws43">Sev<span class="_2 blank"></span>eral graphical devices will b<span class="_9 blank"> </span>e adopted in order to render the read-</div><div class="t m0 x4 h1a y58 ffa fs13 fc4 sc0 ls25 ws44">ing more pleasan<span class="_2 blank"></span>t. W<span class="_3 blank"></span>e will rep<span class="_9 blank"> </span>ort in the margin the <span class="ffb ls0 ws45">MA<span class="_3 blank"></span>TLAB <span class="ffa ls24">command</span></span></div><div class="t m0 x4 h1a y59 ffa fs13 fc4 sc0 ls1f ws46">along side the line where that command is b<span class="_9 blank"> </span>eing in<span class="_2 blank"></span>tro<span class="_9 blank"> </span>duced for the \ufb01rst</div><div class="t m0 x4 h1e y5a ffa fs13 fc4 sc0 ls25 ws47">time.<span class="_b blank"> </span>The<span class="_b blank"> </span>sym<span class="_2 blank"></span>b ol<span class="_c blank"> </span><span class="ls1f ws48 v0">will b<span class="_9 blank"> </span>e used to indicate the presence of exercises,</span></div><div class="t m0 x4 h1f y5b ffa fs13 fc4 sc0 ls25 ws47">the<span class="_d blank"> </span>sym<span class="_2 blank"></span>b ol<span class="_e blank"> </span><span class="ws49 v0">to indicate the presence of a MA<span class="_3 blank"></span>TLAB program, while</span></div><div class="t m0 x6 h20 y5c ffe fs16 fc4 sc0 ls23">1<span class="fff fs17 ls0 ws4a v4">MA<span class="_3 blank"></span>TLAB is a trademark of TheMathW<span class="_3 blank"></span>orks Inc., 24 Prime Park W<span class="_3 blank"></span>ay<span class="_3 blank"></span>, Nat-</span></div><div class="t m0 x13 h21 y5d fff fs17 fc4 sc0 ls26 ws4b">ic<span class="_2 blank"></span>k, MA 01760, T<span class="_3 blank"></span>el: 001+508-647-7000, F<span class="_2 blank"></span>ax: 001+508-647-7001.</div><div class="c x2 y2 w2 h3"><div class="t m0 x0 h4 y3 ff2 fs1 fc5 sc0 ls0">www.TheSolutionManual.com</div></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,-77.810000,-87.930000]}'></div></div> <div id="pfa" class="pf w0 h0" data-page-no="a"><div class="pc pca w0 h0"><img fetchpriority="low" loading="lazy" class="bi x14 y5e w7 h22" alt="" src="https://files.passeidireto.com/00e005a5-168f-4109-be01-2837bb8b1d4a/bga.png"><div class="t m0 x4 h21 y5f fff fs17 fc4 sc0 ls27 ws4c">V<span class="_2 blank"></span>III Pr<span class="_2 blank"></span>e<span class="_2 blank"></span>fa<span class="_2 blank"></span>c<span class="_2 blank"></span>e</div><div class="t m0 x4 h1a y60 ffa fs13 fc4 sc0 ls25 ws4d">the sym<span class="_2 blank"></span>b<span class="_9 blank"> </span>ol<span class="_f blank"> </span>will b<span class="_9 blank"> </span>e used when w<span class="_2 blank"></span>e w<span class="_2 blank"></span>ant to attract the atten<span class="_2 blank"></span>tion of</div><div class="t m0 x4 h1a y61 ffa fs13 fc4 sc0 ls25 ws4d">the reader on a critical or surprising b<span class="_9 blank"> </span>eha<span class="_2 blank"></span>vior of an algorithm or a pro-</div><div class="t m0 x4 h1a y62 ffa fs13 fc4 sc0 ls1f ws4e">cedure. The mathematical formulae of special relev<span class="_2 blank"></span>ance are put within a</div><div class="t m0 x4 h1a y63 ffa fs13 fc4 sc0 ls25 ws4f">frame. Finally<span class="_3 blank"></span>, the symbol<span class="_10 blank"> </span><span class="ls1f ws50 v0">indicates the presence of a displa<span class="_2 blank"></span>y panel</span></div><div class="t m0 x4 h1a y64 ffa fs13 fc4 sc0 ls1f ws51">summarizing concepts and conclusions whic<span class="_2 blank"></span>h hav<span class="_2 blank"></span>e just been rep<span class="_9 blank"> </span>orted</div><div class="t m0 x4 h1a y65 ffa fs13 fc4 sc0 ls0 ws0">and dra<span class="_2 blank"></span>wn.</div><div class="t m0 x12 h1a y66 ffa fs13 fc4 sc0 ls25 ws52">A<span class="_2 blank"></span>t the end of each c<span class="_2 blank"></span>hapter a speci\ufb01c section is devoted to men<span class="_2 blank"></span>tioning</div><div class="t m0 x4 h1a y67 ffa fs13 fc4 sc0 ls1f ws53">those sub<span class="_9 blank"> </span>jects which ha<span class="_2 blank"></span>v<span class="_2 blank"></span>e not b<span class="_9 blank"> </span>een addressed and indicate the biblio-</div><div class="t m0 x4 h1a y68 ffa fs13 fc4 sc0 ls1f ws54">graphical references for a more comprehensiv<span class="_2 blank"></span>e treatment of the material</div><div class="t m0 x4 h1a y69 ffa fs13 fc4 sc0 ls1f ws55">that w<span class="_2 blank"></span>e hav<span class="_2 blank"></span>e carried out.</div><div class="t m0 x12 h1a y6a ffa fs13 fc4 sc0 ls1f ws56">Quite often w<span class="_2 blank"></span>e will refer to the textb<span class="_9 blank"> </span>o<span class="_9 blank"> </span>ok [QSS06] where man<span class="_2 blank"></span>y issues</div><div class="t m0 x4 h1a y6b ffa fs13 fc4 sc0 ls1f ws57">faced in this b<span class="_9 blank"> </span>ook are treated at a deep<span class="_9 blank"> </span>er level, and where theoretical re-</div><div class="t m0 x4 h1a y6c ffa fs13 fc4 sc0 ls1f ws58">sults are pro<span class="_2 blank"></span>ven. F<span class="_3 blank"></span>or a more thorough description of <span class="ffb ls0 ws59">MA<span class="_3 blank"></span>TLAB <span class="ffa ls28 ws5a">we<span class="_b blank"> </span>re f e r</span></span></div><div class="t m0 x4 h1a y6d ffa fs13 fc4 sc0 ls25 ws4f">to [HH05]. All the programs in<span class="_2 blank"></span>tro<span class="_9 blank"> </span>duced in this text can b<span class="_9 blank"> </span>e do<span class="_2 blank"></span>wnloaded</div><div class="t m0 x4 h1a y6e ffa fs13 fc4 sc0 ls1f ws55">from the w<span class="_2 blank"></span>eb address</div><div class="t m0 x15 h23 y6f ff10 fs13 fc4 sc0 ls1f">mox.polimi.it/qs</div><div class="t m0 x12 h1a y70 ffa fs13 fc4 sc0 ls25 ws5b">No sp<span class="_9 blank"> </span>ecial prerequisite is demanded of the reader, with the exception</div><div class="t m0 x4 h1a y71 ffa fs13 fc4 sc0 ls25 ws5c">of an elemen<span class="_2 blank"></span>tary course of Calculus.</div><div class="t m0 x12 h1a y72 ffa fs13 fc4 sc0 ls0 ws5d">Ho<span class="_2 blank"></span>wev<span class="_2 blank"></span>er, in the course of the \ufb01rst c<span class="_2 blank"></span>hapter, we recall the principal re-</div><div class="t m0 x4 h1a y73 ffa fs13 fc4 sc0 ls25 ws5e">sults of Calculus and Geometry that will b<span class="_9 blank"> </span>e used extensiv<span class="_2 blank"></span>ely throughout</div><div class="t m0 x4 h1a y74 ffa fs13 fc4 sc0 ls1f ws5f">this text. The less elemen<span class="_2 blank"></span>tary sub<span class="_11 blank"> </span>jects, those whic<span class="_2 blank"></span>h are not so neces-</div><div class="t m0 x4 h1a y75 ffa fs13 fc4 sc0 ls1f ws4e">sary for an in<span class="_2 blank"></span>tro<span class="_9 blank"> </span>ductory educational path, are highligh<span class="_2 blank"></span>ted by the special</div><div class="t m0 x4 h24 y76 ffa fs13 fc4 sc0 ls25 ws47">sym<span class="_2 blank"></span>b ol<span class="_12 blank"> </span><span class="ls0 v0">.</span></div><div class="t m0 x12 h1a y77 ffa fs13 fc4 sc0 ls1f ws51">W<span class="_3 blank"></span>e express our thanks to Thanh-Ha Le Thi from Springer-V<span class="_3 blank"></span>erlag</div><div class="t m0 x4 h1a y78 ffa fs13 fc4 sc0 ls1f ws60">Heidelb<span class="_9 blank"> </span>erg, and to F<span class="_3 blank"></span>rancesca Bonadei and Marina F<span class="_3 blank"></span>orlizzi from Springer-</div><div class="t m0 x4 h1a y79 ffa fs13 fc4 sc0 ls25 ws61">Italia for their friendly collab<span class="_9 blank"> </span>oration throughout this pro<span class="_9 blank"> </span>ject. W<span class="_3 blank"></span>e grate-</div><div class="t m0 x4 h1a y7a ffa fs13 fc4 sc0 ls25 ws62">fully thank Prof. Eastham of Cardi\ufb00 Univ<span class="_2 blank"></span>ersity for editing the<span class="_13 blank"> </span>language</div><div class="t m0 x4 h1a y7b ffa fs13 fc4 sc0 ls25 ws63">of the whole man<span class="_2 blank"></span>uscript and stimulating us to clarify man<span class="_2 blank"></span>y points of our</div><div class="t m0 x4 h1a y7c ffa fs13 fc4 sc0 ls24">text.</div><div class="t m0 x4 h1a y7d ffa fs13 fc4 sc0 ls1f ws55">Milano and Lausanne<span class="_14 blank"> </span><span class="ff8 ws64">Al\ufb01o Quarter<span class="_3 blank"></span>oni</span></div><div class="t m0 x4 h1a y7e ffa fs13 fc4 sc0 ls25 ws5c">Ma<span class="_2 blank"></span>y 2003<span class="_15 blank"> </span><span class="ff8 ls20 ws65">F<span class="_3 blank"></span>austo Saleri</span></div><div class="t m0 x4 h1a y7f ff8 fs13 fc4 sc0 ls0 ws0">Pr<span class="_2 blank"></span>efac<span class="_3 blank"></span>e to the Se<span class="_2 blank"></span>c<span class="_2 blank"></span>ond Edition</div><div class="t m0 x12 h1a y80 ffa fs13 fc4 sc0 ls1f ws66">In this second edition w<span class="_2 blank"></span>e hav<span class="_2 blank"></span>e enric<span class="_2 blank"></span>hed all the Chapters b<span class="_2 blank"></span>y intro-</div><div class="t m0 x4 h1a y81 ffa fs13 fc4 sc0 ls0 ws67">ducing sev<span class="_2 blank"></span>eral new problems. Moreov<span class="_2 blank"></span>er, w<span class="_2 blank"></span>e ha<span class="_2 blank"></span>ve added new methods</div><div class="t m0 x4 h1a y82 ffa fs13 fc4 sc0 ls25 ws38">for the n<span class="_2 blank"></span>umerical solution of linear and nonlinear systems, the eigen-</div><div class="t m0 x4 h1a y83 ffa fs13 fc4 sc0 ls25 ws68">v<span class="_2 blank"></span>alue computation and the solution of initial-v<span class="_3 blank"></span>alue problems. Another</div><div class="t m0 x4 h1a y84 ffa fs13 fc4 sc0 ls1f ws69">relev<span class="_2 blank"></span>an<span class="_2 blank"></span>t impro<span class="_2 blank"></span>v<span class="_2 blank"></span>ement is that w<span class="_2 blank"></span>e also use the Octa<span class="_2 blank"></span>v<span class="_2 blank"></span>e programming en-</div><div class="t m0 x4 h1a y85 ffa fs13 fc4 sc0 ls25 ws6a">vironmen<span class="_2 blank"></span>t. Octav<span class="_2 blank"></span>e is a reimplemen<span class="_2 blank"></span>tation of part of <span class="ffb ls0 ws6b">MA<span class="_3 blank"></span>TLAB <span class="ffa ls24 ws6c">which</span></span></div><div class="c x2 y2 w2 h3"><div class="t m0 x0 h4 y3 ff2 fs1 fc5 sc0 ls0">www.TheSolutionManual.com</div></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,-77.810000,-87.930000]}'></div></div>
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