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				<div style="text-align:left;margin-bottom:20px;">  		</div><span itemprop="name" class="title">Numerische Mathematik 1<br></span><span class="subtitle">Stationäre Probleme. Eine Einführung anhand von Differentialgleichungsproblemen<br></span><p>Autoren:<br><span itemprop="author" class="author"><b>Walter Zulehner</b></span></p><p>Verlag:<br><b itemprop="publisher">Springer Basel AG</b>&nbsp;&nbsp;<a onclick="SearchPublEnt(282)" href="#">Weitere Titel dieses Verlages anzeigen</a></p>		
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<span class="notbold">Erschienen: </span>Dezember 2007<br><span class="notbold">Seiten: </span>150<br><span class="notbold">Sprache: </span>Deutsch<br><span class="notbold">Preis: </span>18.90 €<br>
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						<div class="right-td"><span class="notbold">Ma&szlig;e: </span>242x165x12<br><span class="notbold">Einband: </span>Taschenbuch<br><span class="notbold">Reihe: </span>Mathematik kompakt<br><span class="notbold">ISBN: </span>9783764384265			</div>
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						<h1><a href="_9783764384265_inhalt.html">Inhaltsverzeichnis</a></h1>
						<p><table border="0" style="width: 100%; text-align: left;" class="htmltd"><tbody><tr><td colspan="7" style="line-height: 4px; font-size: 4px;" class="htmltd"> </td></tr><tr><td colspan="7" style="padding-bottom: 10px; font-weight: bold; text-align: left;" class="htmltd">Inhaltsverzeichnis</td></tr><tr><td colspan="7" style="line-height: 4px; font-size: 4px;" class="htmltd"> </td></tr><tr><td colspan="6" style="vertical-align: top; font-weight: bold;" class="htmltd">Vorwort</td><td style="text-align: right; font-weight: bold;" class="htmltd">vi</td></tr><tr><td colspan="7" style="line-height: 4px; font-size: 4px;" class="htmltd"> </td></tr><tr><td colspan="6" style="vertical-align: top; font-weight: bold;" class="htmltd">Einleitung</td><td style="vertical-align: top; text-align: right; font-weight: bold;" class="htmltd">1</td></tr><tr><td colspan="7" style="line-height: 4px; font-size: 4px;" class="htmltd"> </td></tr><tr><td style="vertical-align: top; font-weight: bold;" class="htmltd">1</td><td colspan="5" style="vertical-align: top; font-weight: bold;" class="htmltd">Ein
erstes
Beispiel
einer
Variationsformulierung</td><td style="vertical-align: top; text-align: right; font-weight: bold;" class="htmltd">7</td></tr><tr><td colspan="7" style="line-height: 4px; font-size: 4px;" class="htmltd"> </td></tr><tr><td style="vertical-align: top; font-weight: bold;" class="htmltd">2</td><td colspan="5" style="vertical-align: top; font-weight: bold;" class="htmltd">Der
Satz
von
Lax-Milgram</td><td style="vertical-align: top; text-align: right; font-weight: bold;" class="htmltd">19</td></tr><tr><td colspan="7" style="line-height: 4px; font-size: 4px;" class="htmltd"> </td></tr><tr><td style="vertical-align: top; font-weight: bold;" class="htmltd">3</td><td colspan="5" style="vertical-align: top; font-weight: bold;" class="htmltd">Die
Galerkin-Methode</td><td style="vertical-align: top; text-align: right; font-weight: bold;" class="htmltd">35</td></tr><tr><td class="htmltd"> </td><td style="vertical-align: top;" class="htmltd">4.1</td><td colspan="4" style="vertical-align: top;" class="htmltd">Ein
Beispiel
einer
Finite-Elemente-Methode</td><td style="vertical-align: top; text-align: right;" class="htmltd">36</td></tr><tr><td class="htmltd"> </td><td style="vertical-align: top;" class="htmltd">4.2</td><td colspan="4" style="vertical-align: top;" class="htmltd">Der
Diskretisierungsfehler</td><td style="vertical-align: top; text-align: right;" class="htmltd">44</td></tr><tr><td colspan="7" style="line-height: 4px; font-size: 4px;" class="htmltd"> </td></tr><tr><td style="vertical-align: top; font-weight: bold;" class="htmltd">5</td><td colspan="5" style="vertical-align: top; font-weight: bold;" class="htmltd">Lineare
Gleichungssysteme</td><td style="vertical-align: top; text-align: right; font-weight: bold;" class="htmltd">53</td></tr><tr><td class="htmltd"> </td><td style="vertical-align: top;" class="htmltd">5.1</td><td colspan="4" style="vertical-align: top;" class="htmltd">Kondition
des
Problems</td><td style="vertical-align: top; text-align: right;" class="htmltd">53</td></tr><tr><td class="htmltd"> </td><td style="vertical-align: top;" class="htmltd">5.2</td><td colspan="4" style="vertical-align: top;" class="htmltd">Konditionszahl
der
Steifigkeitsmatrix</td><td style="vertical-align: top; text-align: right;" class="htmltd">60</td></tr><tr><td colspan="7" style="line-height: 4px; font-size: 4px;" class="htmltd"> </td></tr><tr><td style="vertical-align: top; font-weight: bold;" class="htmltd">6</td><td colspan="5" style="vertical-align: top; font-weight: bold;" class="htmltd">Das
Gaußsche
Eliminationsverfahren</td><td style="vertical-align: top; text-align: right; font-weight: bold;" class="htmltd">65</td></tr><tr><td class="htmltd"> </td><td style="vertical-align: top;" class="htmltd">6.1</td><td colspan="4" style="vertical-align: top;" class="htmltd">Der
Algorithmus</td><td style="vertical-align: top; text-align: right; font-style: italic;" class="htmltd">65</td></tr><tr><td class="htmltd"> </td><td style="vertical-align: top;" class="htmltd">6.2</td><td colspan="4" style="vertical-align: top;" class="htmltd">Numerische
Stabilität
des
Algorithmus</td><td style="vertical-align: top; text-align: right;" class="htmltd">75</td></tr><tr><td colspan="7" style="line-height: 4px; font-size: 4px;" class="htmltd"> </td></tr><tr><td style="vertical-align: top; font-weight: bold;" class="htmltd">7</td><td colspan="5" style="vertical-align: top; font-weight: bold;" class="htmltd">Erweiterung
auf
lineare
mehrdimensionale
Randwertprobleme</td><td style="vertical-align: top; text-align: right; font-weight: bold;" class="htmltd">83</td></tr><tr><td colspan="7" style="line-height: 4px; font-size: 4px;" class="htmltd"> </td></tr><tr><td style="vertical-align: top; font-weight: bold;" class="htmltd">8</td><td colspan="5" style="vertical-align: top; font-weight: bold;" class="htmltd">Iterative
Verfahren
für
lineare
Gleichungssysteme</td><td style="vertical-align: top; text-align: right; font-weight: bold;" class="htmltd">93</td></tr><tr><td class="htmltd"> </td><td style="vertical-align: top;" class="htmltd">8.1</td><td colspan="4" style="vertical-align: top;" class="htmltd">Das
Richardson-Verfahren</td><td style="vertical-align: top; text-align: right;" class="htmltd">93</td></tr><tr><td class="htmltd"> </td><td style="vertical-align: top;" class="htmltd">8.2</td><td colspan="4" style="vertical-align: top;" class="htmltd">Das
Gradientenverfahren</td><td style="vertical-align: top; text-align: right;" class="htmltd">99</td></tr><tr><td class="htmltd"> </td><td style="vertical-align: top;" class="htmltd">8.3</td><td colspan="4" style="vertical-align: top;" class="htmltd">Das
Verfahren
der
konjugierten
Gradienten</td><td style="vertical-align: top; text-align: right;" class="htmltd">103</td></tr><tr><td class="htmltd"> </td><td style="vertical-align: top;" class="htmltd">8.4</td><td colspan="4" style="vertical-align: top;" class="htmltd">Präkonditionierung</td><td style="vertical-align: top; text-align: right;" class="htmltd">112</td></tr><tr><td colspan="7" style="line-height: 4px; font-size: 4px;" class="htmltd"> </td></tr><tr><td style="vertical-align: top; font-weight: bold;" class="htmltd">9</td><td colspan="5" style="vertical-align: top; font-weight: bold;" class="htmltd">Erweiterung
auf
nichtlineare
Randwertprobleme</td><td style="vertical-align: top; text-align: right; font-weight: bold;" class="htmltd">127</td></tr><tr><td colspan="7" style="line-height: 4px; font-size: 4px;" class="htmltd"> </td></tr><tr><td style="vertical-align: top; font-weight: bold;" class="htmltd">10</td><td colspan="5" style="vertical-align: top; font-weight: bold;" class="htmltd">Das
Newton-Verfahren</td><td style="vertical-align: top; text-align: right; font-weight: bold;" class="htmltd">135</td></tr><tr><td colspan="6" style="vertical-align: top; font-weight: bold;" class="htmltd">Literaturverzeichnis</td><td style="vertical-align: top; text-align: right; font-weight: bold;" class="htmltd">147</td></tr><tr><td colspan="6" style="vertical-align: top; font-weight: bold;" class="htmltd">Index</td><td style="vertical-align: top; text-align: right; font-weight: bold;" class="htmltd">149</td></tr></tbody></table><br /><br /><br /></p>
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						<p><blockquote><table-sv></table-sv><p><b>Index </b></p><br /><a name=A><font><b>A</b></font></a><p style="margin: 0px; padding: 0px;">Ableitung <br /> - schwache 10<br />Abschließungsprinzip 32<br />Algorithmus 11<br />A-orthogonal 50, 105 </p><br /><a name=B><font><b>B</b></font></a><p style="margin: 0px; padding: 0px;">Banachscher Fixpunktsatz 23<br />Bandbreite 73<br />Bandmatrix 72<br />Bilanzgleichung 2<br /> - Bilinearform 14 <br />beschränkte, V-beschränkte 25 <br /> - elliptische, V-elliptische 25 <br /> - nicht-negative 29 <br /> - symmetrische 29 </p><br /><a name=C><font><b>C</b></font></a><p style="margin: 0px; padding: 0px;">C<sub>0</sub>°°(0, 1) 10<br />Cholesky-Zerlegung 74 </p><br /><a name=D><font><b>D</b></font></a><p style="margin: 0px; padding: 0px;">Divergenz 3 <br />Divergenzform 7, 84, 127<br />Dreieckszerlegung 71 <br /> - für Bandmatrizen 72 <br /> - für symmetrische und positiv definite Matrizen 74 </p><br /><a name=E><font><b>E</b></font></a><p style="margin: 0px; padding: 0px;">elementare Operation 11<br />Energiefunktional 30 </p><br /><a name=F><font><b>F</b></font></a><p style="margin: 0px; padding: 0px;">Fehler <br /> - absoluter 29 <br /> - Approximations46 <br /> - Daten19 <br /> - Diskretisierungs44 <br /> - Interpolations47 <br /> - relativer 29 <br /> - Rundungs75 <br /> - unvermeidbarer 76 <br /> - Verfahrens44<br />Finite-Differenzen-Methode 8, 43<br />Finite-Elemente-Methode 36, 87 <br />Fixpunktgleichung 24<br />Fixpunktiteration 24<br />Fluss 3, 127<br />Friedrichs-Ungleichung 32, 87 </p><br /><a name=G><font><b>G</b></font></a><p style="margin: 0px; padding: 0px;">Galerkin-Methode 35<br />Galerkin-Orthogonalität 46<br />gestaffeltes System 72<br />Gitter siehe Zerlegung Gitterpunkte siehe Knoten Gradient 4 <br /> - schwacher 85 </p><br /><a name=H><font><b>H</b></font></a><p style="margin: 0px; padding: 0px;">H<sup>1</sup> (0, 1) 12<br />H<sup>1</sup> (om) 85<br />H<sup>2</sup> (0, 1) 48 </p><br /><a name=K><font><b>K</b></font></a><p style="margin: 0px; padding: 0px;">Knoten 36, 88 <br />Knotenbasis 37, 88 <br />konditioniert gut 29<br />schlecht 29 <br />Konditionszahl <br /> - einer Matrix 54<br />- eines Operators 29 <br />konjugierte Richtungen 105 <br />Konvergenz lokale 137<br />- q-lineare 28<br />- q-quadratische 138<br />- q-superlineare 137<br />- r-lineare 28<br />- r-quadratische 139 <br />Konvergenzrate 28 <br />korrekt gestelltes Problem 19 <br />Krylow-Unterräum 104<br />Krylow-Methode 111 </p><br /><a name=L><font><b>L</b></font></a><p style="margin: 0px; padding: 0px;">Lastvektor 38, 88<br />Liniensuchverfahren 100 <br />lokaler Träger 37, 88 </p><br /><a name=M><font><b>M</b></font></a><p style="margin: 0px; padding: 0px;">Massenmatrix 62 <br /> - Element62<br />Matrix <br /> - adjungierte 57 <br /> - dünnbesetzte 39 <br /> - selbstadjungierte 57<br />MFLOPS 68 </p><br /><a name=N><font><b>N</b></font></a><p style="margin: 0px; padding: 0px;">nnz(M) 91<br />Norm <br /> - einer Matrix 53 <br /> - eines linearen Funktionais 21 <br /> - eines linearen Operators 28 <br /> - Energie99 <br /> - euklidische 39 <br /> - H<sup>1</sup> 12, 85 <br /> - H<sup>2</sup> 48 <br /> - L<sub>2</sub> 12, 85 <br /> - Residuums99 </p><br /><a name=O><font><b>O</b></font></a><p style="margin: 0px; padding: 0px;">Operator <br /> - Lipschitz-stetiger 129<br />- monotoner 134<br />- stark monotoner 129 </p><br /><a name=P><font><b>P</b></font></a><p style="margin: 0px; padding: 0px;">Pivotelement 65, 67, 68<br />Pivotsuche <br /> - Spalten79 <br /> - Total79<br />Pk, Polynome vom Grad &lt;= k 36<br />Poincare-Ungleichung 34 </p><br /><a name=R><font><b>R</b></font></a><p style="margin: 0px; padding: 0px;">Randbedingung 4 <br /> - Dirichlet7, 83 <br /> - natürliche 10 <br /> - Neumann7, 83 <br />Robin17 <br /> - wesentliche 10<br />Randwertproblem 4 <br /> - klassische Formulierung 8 <br /> - klassische Lösung 8 <br /> - lineares <br /> - eindimensionales 7 mehrdimensionales 83 <br /> - nichtlineares 127 <br /> - schwache Lösung 14 <br /> - Variationsformulierung 14, 85, 128<br />Raumaufspaltung 117 <br /> - hierarchische 121<br />Rayleigh-Quotient 59 <br />Rayleigh-Ritz-Methode 36<br />Referenzelement 40, 88<br />Riesz-Isomorphismus 22<br />Rieszscher Darstellungssatz 21<br />Ritzsches Energiefunktional 30 </p><br /><a name=S><font><b>S</b></font></a><p style="margin: 0px; padding: 0px;">Satz <br /> - Banachscher Fixpunkt23 <br /> - Rieszscher Darstellungs21 <br /> - von Cea 45 <br /> - von Lax-Milgram 25, 129<br />Schwarz-Methode <br /> - additive 117 <br /> - multiplikative 118<br />Skalarprodukt <br /> - Energie99 <br /> - euklidisches 3, 39 <br /> - H<sup>1</sup><sup></sup> 12, 85 <br /> - L<sub>2</sub> 12, 85<br />Sobolew-Raum 12, 48, 85, 129<br />Spuroperator 14, 85<br />stabil <br /> - daten29 <br /> - numerisch 78<br />Steifigkeitsmatrix 38, 88 <br /> - Element40, 88 </p><br /><a name=U><font><b>U</b></font></a><p style="margin: 0px; padding: 0px;">Unterraum-Korrektur-Gleichung 117<br />Unterraum-Korrektur-Methoden 116 </p><br /><a name=V><font><b>V</b></font></a><p style="margin: 0px; padding: 0px;">Verfahren <br /> - CG105<br />- direktes 75<br />- Gauß-Seidel120<br />- Gaußsches Eliminations65 <br /> - für Bandmatrizen 74<br />- GMRES111<br />- Gradienten101<br />- Jacobi118<br />- Mehrgitter124<br />- Newton136 <br /> - gedämpftes 144 <br />vereinfachtes 146<br />- optimales 91<br />- PCG125 <br /> - präkonditioniertes CG125<br />- präkonditioniertes Richardson112<br />- Richardson93<br />von optimaler Komplexität 91<br />- Zweigitter123 </p><br /><a name=Z><font><b>Z</b></font></a><p style="margin: 0px; padding: 0px;">Zerlegung 36, 87 </p></blockquote><br /><br /></p>
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