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<td class="medium-text" colspan="3"><strong>A Block Lanczos Method for Computing the Singular Values and Corresponding Singular Vectors of a Matrix</strong></td>
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<SPAN class="mediumb-text">ACM Transactions on Mathematical Software (TOMS) </span>
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<span class="small-text"> Volume 7 , Issue 2 (June 1981)</span>
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Pages: 149 - 169
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Year of Publication: 1981
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ISSN:0098-3500
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<a href=äuthor_page.cfm?id=81332501126&coll=GUIDE&dl=GUIDE&trk=0&CFID=46721426&CFTOKEN=31610041" target="_self">Gene H. Golub</a>
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<small> Department of Computer Science, Cornell University, Ithaca, NY</small>
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<a href=äuthor_page.cfm?id=81100307341&coll=GUIDE&dl=GUIDE&trk=0&CFID=46721426&CFTOKEN=31610041" target="_self">Franklin T. Luk</a>
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<small> Department of Computer Science, Cornell University, Ithaca, NY</small>
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<a href=äuthor_page.cfm?id=81100392276&coll=GUIDE&dl=GUIDE&trk=0&CFID=46721426&CFTOKEN=31610041" target="_self">Michael L. Overton</a>
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<small> Courant Institute of Mathematical Sciences, New York University, New York</small>
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PAIGE, C.C Bidiagonahzation of matrices and solution of hnear equations. SIAM J. Numer. Anal. 11 (1974), 197-209.
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14
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<a href="citation.cfm?id=907375&dl=GUIDE&coll=GUIDE&CFID=46721426&CFTOKEN=31610041">
John Franklin Palmer, II, Conjugate-direction methods and parallel-computing., 1974
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15
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<div class=äbstract">
RUHE, A. Implementation aspects of band Lanczos algorithms for computation of elgenvalues of large sparse symmetric matrices Rep., Dep of Mathematics, Umv. California, San Diego, Feb. 1978.
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16
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RUTISHAUSER, H. On Jacobi rotation patterns. In Proc. Syrup. Applled Math, vol. 15, 1963, pp. 219-239.
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17
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<div class=äbstract">
STEWART, G W. Error and perturbation bounds for subspaces associated with certain elgenvalue problems. SIAM Rev 15 (1973), 727-764
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<div class=äbstract">
18
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<div class=äbstract">
<a href="citation.cfm?id=907075&dl=GUIDE&coll=GUIDE&CFID=46721426&CFTOKEN=31610041">
Richard Ray Underwood, An iterative block lanczos method for the solution of large sparse symmetric eigenproblems., 1975
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<div class=äbstract">
19
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<div class=äbstract">
<a href="citation.cfm?id=906731&dl=GUIDE&coll=GUIDE&CFID=46721426&CFTOKEN=31610041">
Charles Francis Van Loan, Generalized singular values with algorithms and applications., 1973
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<td valign="top"> </td>
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<div class=äbstract">
20
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</td>
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<div class=äbstract">
<a href="citation.cfm?id=59657&dl=GUIDE&coll=GUIDE&CFID=46721426&CFTOKEN=31610041">
J. H. Wilkinson, The algebraic eigenvalue problem, Oxford University Press, Inc., New York, NY, 1988
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<div class=äbstract">
<A HREF="citation.cfm?id=355945.355946#CIT"><img name="top" src="http://portal.acm.org/images/arrowu.gif" hspace="10" border="0"></A><SPAN class=heading><A NAME="citings">CITED BY</A><A NAME="citedby"></A> <i>2</i></span>
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<tr valign="top">
<td valign="top">
</td>
<td>
<div class=äbstract">
<a href="citation.cfm?id=1241428&dl=GUIDE&coll=GUIDE&CFID=46721426&CFTOKEN=31610041">
Gang Wu, A modified harmonic block Arnoldi algorithm with adaptive shifts for large interior eigenproblems, Journal of Computational and Applied Mathematics, v.205 n.1, p.343-363, August, 2007
</a>
</div>
</td>
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<td valign="top">
<img src="http://portal.acm.org/images/ACM_mini.jpg" width="25" height="24" alt="" vspace="0" border="0" align="top">
</td>
<td>
<div class=äbstract">
<a href="citation.cfm?id=237622&dl=GUIDE&coll=GUIDE&CFID=46721426&CFTOKEN=31610041">
E. M. Garzon , I. García, Parallel implementation of the Lanczos method for sparse matrices: analysis of data distributions, Proceedings of the 10th international conference on Supercomputing, p.294-300, May 25-28, 1996, Philadelphia, Pennsylvania, United States
</a>
</div>
</td>
</tr>
</table>
</div>
<br>
<div class="indterms">
<A HREF="citation.cfm?id=355945.355946#CIT"><img name="top" src="http://portal.acm.org/images/arrowu.gif" hspace="10" border="0"></A><SPAN class=heading><A NAME="IndexTerms">INDEX TERMS</A></span>
<p class="Categories">
<SPAN class=heading><A NAME="GenTerms">Primary Classification:</A></span>
<br>
<b>G.</b>
<a href="results.cfm?query=PrimaryCCS%3AG&querydisp=PrimaryCCS%3AG&termshow=matchboolean&coll=GUIDE&dl=GUIDE&CFID=46721426&CFTOKEN=31610041" target="_self">
Mathematics of Computing</a><br>
<img src="http://portal.acm.org/images/tree.gif" border="0" height="20" width="20">
<b>G.1</b>
<a href="results.cfm?query=PrimaryCCS%3AG1&querydisp=PrimaryCCS%3AG1&termshow=matchboolean&coll=GUIDE&dl=GUIDE&CFID=46721426&CFTOKEN=31610041" target="_self">
NUMERICAL ANALYSIS</a><br>
<img src="http://portal.acm.org/images/tree.gif" border="0" height="20" width="20">
<b>G.1.3</b>
<a href="results.cfm?query=PrimaryCCS%3AG13&querydisp=PrimaryCCS%3AG13&termshow=matchboolean&coll=GUIDE&dl=GUIDE&CFID=46721426&CFTOKEN=31610041" target="_self">
Numerical Linear Algebra</a><br>
<img src="http://portal.acm.org/images/tree.gif" border="0" height="20" width="20">
<b>Subjects:</b>
<a href="results.cfm?query=PrimarySubject%3A%22Sparse%2C%20structured%2C%20and%20very%20large%20systems%20%28direct%20and%20iterative%20methods%29%22&querydisp=PrimarySubject%3A%22Sparse%2C%20structured%2C%20and%20very%20large%20systems%20%28direct%20and%20iterative%20methods%29%22&termshow=matchboolean&coll=GUIDE&dl=GUIDE&CFID=46721426&CFTOKEN=31610041" target="_self">Sparse, structured, and very large systems (direct and iterative methods)</a>
<br>
</p>
<p class="Categories">
<SPAN class=heading><A NAME="GenTerms">Additional Classification:</A></span>
<br>
<b>F.</b>
<a href="results.cfm?query=CCS%3AF&querydisp=CCS%3AF&termshow=matchboolean&coll=GUIDE&dl=GUIDE&CFID=46721426&CFTOKEN=31610041" target="_self">
Theory of Computation</a><br>
<img src="http://portal.acm.org/images/tree.gif" border="0" height="20" width="20">
<b>F.2</b>
<a href="results.cfm?query=CCS%3AF2&querydisp=CCS%3AF2&termshow=matchboolean&coll=GUIDE&dl=GUIDE&CFID=46721426&CFTOKEN=31610041" target="_self">
ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY</a><br>
<img src="http://portal.acm.org/images/tree.gif" border="0" height="20" width="20">
<b>F.2.1</b>
<a href="results.cfm?query=CCS%3AF21&querydisp=CCS%3AF21&termshow=matchboolean&coll=GUIDE&dl=GUIDE&CFID=46721426&CFTOKEN=31610041" target="_self">
Numerical Algorithms and Problems</a><br>
<img src="http://portal.acm.org/images/tree.gif" border="0" height="20" width="20">
<b>Subjects:</b>
<a href="results.cfm?query=Subject%3A%22Computations%20on%20matrices%22&querydisp=Subject%3A%22Computations%20on%20matrices%22&termshow=matchboolean&coll=GUIDE&dl=GUIDE&CFID=46721426&CFTOKEN=31610041" target="_self">Computations on matrices</a>
<br>
</p>
<br>
<p class="GenTerms">
<SPAN class=heading><A NAME="GenTerms">General Terms:</A></span>
<BR>
<a href="results.cfm?query=General%20Terms%3A%22Algorithms%22&querydisp=General%20Terms%3A%22Algorithms%22&termshow=matchboolean&coll=GUIDE&dl=GUIDE&CFID=46721426&CFTOKEN=31610041" target="_self">
Algorithms</a>,
<a href="results.cfm?query=General%20Terms%3A%22Theory%22&querydisp=General%20Terms%3A%22Theory%22&termshow=matchboolean&coll=GUIDE&dl=GUIDE&CFID=46721426&CFTOKEN=31610041" target="_self">
Theory</a>
</p>
</div>
<div class=äbstract">
<A HREF="citation.cfm?id=355945.355946#CIT"><img name="top" src="http://portal.acm.org/images/arrowu.gif" hspace="10" border="0"></A><SPAN class=heading><A NAME="collab">Collaborative Colleagues:</A></span>
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<td>
<div class=äbstract">
Gene H. Golub: <a href=äuthor_page.cfm?id=81332501126&dsp=coll&coll=GUIDE&dl=GUIDE&trk=1&CFID=46721426&CFTOKEN=31610041" target="_self">colleagues</a>
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Franklin T. Luk: <a href=äuthor_page.cfm?id=81100307341&dsp=coll&coll=GUIDE&dl=GUIDE&trk=1&CFID=46721426&CFTOKEN=31610041" target="_self">colleagues</a>
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Michael L. Overton: <a href=äuthor_page.cfm?id=81100392276&dsp=coll&coll=GUIDE&dl=GUIDE&trk=1&CFID=46721426&CFTOKEN=31610041" target="_self">colleagues</a>
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