@book{cullum2002lanczos, author = {Cullum, J.K. and Willoughby, R.A.}, interhash = {cfc97672c78c590391fc6f731d48ddc2}, intrahash = {b6fa6a375178396d472af2006fb21fc8}, publisher = {Society for Industrial Mathematics}, title = {{Lanczos algorithms for large symmetric eigenvalue computations: Theory}}, url = {http://scholar.google.de/scholar.bib?q=info:zshJq2GVHO8J:scholar.google.com/&output=citation&hl=de&ct=citation&cd=0}, year = 2002 } @article{356494, abstract = { Algorithms for sparse Gaussian elimination with partial pivoting
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Algorithms for sparse Gaussian elimination with partial pivoting
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Volume 4 ,  Issue 4  (December 1978) table of contents
Pages: 330 - 338  
Year of Publication: 1978
ISSN:0098-3500
Author
Andrew H Sherman  Department of Computer Sciences, Painter 328, The University of Texas at Austin, Austin, TX
Publisher
ACM  New York, NY, USA
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Downloads (6 Weeks): 2,   Downloads (12 Months): 58,   Citation Count: 2
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REFERENCES
 
1
Alfred V. Aho , John E. Hopcroft, The Design and Analysis of Computer Algorithms, Addison-Wesley Longman Publishing Co., Inc., Boston, MA, 1974
 
2
CURTIS, A.R., AND REID, J.K. FORTRAN subroutines for the solution of sparse sets of hnear equations. AERE Rep. R6844, AERE HarweU, England, 1971.
 
3
CURTIS, A.R, AND REID, J.K The solution of large sparse unsymmetnc systems of hnear equations. Information Processing '71 (1971), 1240-1245.
 
4
DUFF, I.S., AND REID, J.K A comparison of sparsity ordermgs for obtaining a pivotal sequence in Gausslan elm~matlon. AERE Rep. T.P. 526, AERE Harwell, England, 1973
5
Stanley C. Eisenstat , Andrew H. Sherman, Efficient implementation of sparse nonsymmetric Gaussian elimination without pivoting (abstract), ACM SIGNUM Newsletter, v.10 n.4, p.26-29, December 1975  [doi>10.1145/1053205.1053217]
 
6
FORSYTHE, G.E., AND MOLER, C B Computer Solutton of Linear Algebraic Systems Prentice- Hall, Englewood Cliffs, N J, 1967
 
7
Donald E. Knuth, The art of computer programming, volume 3: (2nd ed.) sorting and searching, Addison Wesley Longman Publishing Co., Inc., Redwood City, CA, 1998

CITED BY  2
Andrew H. Sherman, Algorithm 533: NSPIV, a Fortran subroutine for sparse Gaussian elimination with partial pivoting [F4], ACM Transactions on Mathematical Software (TOMS), v.4 n.4, p.391-398, December 1978
Jing Li , Tao Jiang, Efficient rule-based haplotyping algorithms for pedigree data, Proceedings of the seventh annual international conference on Research in computational molecular biology, p.197-206, April 10-14, 2003, Berlin, Germany

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.3 Numerical Linear Algebra
          Subjects: Sparse, structured, and very large systems (direct and iterative methods)

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.3 Numerical Linear Algebra
          Subjects: Linear systems (direct and iterative methods)


General Terms:
Algorithms


Keywords:
analysis of algorithms, linear equations, pivoting algorithms, sparse Gaussian elimination, sparse linear systems

Collaborative Colleagues:
Andrew H Sherman: colleagues

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}, address = {New York, NY, USA}, author = {Sherman, Andrew H}, doi = {http://doi.acm.org/10.1145/356502.356494}, interhash = {abdfc22d990fc6bc077527abf2e2c344}, intrahash = {3d4ed208d8092e541d7c7f4d19d9e607}, issn = {0098-3500}, journal = {ACM Trans. Math. Softw.}, number = 4, pages = {330--338}, publisher = {ACM}, title = {Algorithms for sparse Gaussian elimination with partial pivoting}, url = {http://portal.acm.org/citation.cfm?id=356494}, volume = 4, year = 1978 } @article{berry1993svdpackc, author = {Berry, M. and Do, T. and O’Brien, G. and Krishna, V. and Varadhan, S.}, interhash = {ee044096cd5326538d8e8173c9d41e1a}, intrahash = {f6673604e495c6d457150f6c68cc90b9}, journal = {University of Tennessee}, publisher = {Citeseer}, title = {{SVDPACKC (version 1.0) user's guide}}, url = {http://scholar.google.de/scholar.bib?q=info:Y2fs0GQQ_LIJ:scholar.google.com/&output=citation&hl=de&ct=citation&cd=0}, year = 1993 } @article{binder2005phylogenetic, abstract = {Phylogenetic relationships of resupinate Homobasidiomycetes (Corticiaceae s. lat. and others) were studied using ribosomal DNA (rDNA) sequences from a broad sample of resupinate and nonresupinate taxa. Two datasets were analysed using parsimony, a'core'dataset of 142 species, each of which is represented by four rDNA regions (mitochondrial and nuclear large and small subunits), and a 'full' clataset of 656 species, most of which were represented only by nuclear large subunit rDNA sequences. Both datasets were analysed using traditional heuristic methods with bootstrapping, and the full clataset was also analysed with the Parsimony Ratchet, using equal character weights and six-parameter weighted parsimony. Analyses of both datasets supported monophyly of the eight major clades of Homobasicliomycetes recognised by Hibbett and Thorn, as well as independent lineages corresponding to the Gloeophyllum clade, corticioid clade and jaapia argillacea. Analyses of the full clataset resolved two additional groups, the athelioid clade and trechisporoid clade (the latter may be nested in the polyporoid clade). Thus, there are at least 12 independent clades of Homobasicliomycetes. Higher-level relationships among the major clades are not resolved with confidence. Nevertheless, the euagarics clade, bolete clade, athelioid clade and jaapia argillacea are consistently resolved as a monophyletic group, whereas the cantharelloid clade, gomphoid-phalloid clade and hymenochaetoid clade are placed at the base of the Homobasidiomycetes, which is consistent with the preponderance of imperforate parenthesomes in those groups. Resupinate forms occur in each of the major clades of Homobasidiomycetes, some of which are composed mostly or exclusively of resupinate forms (athelioid clade, corticioid clade, trechisporoid clade,jaapia). The largest concentrations of resupinate forms occur in the polyporoid clade, russuloid clade and hymenochaetoid clade. The cantharelloid clade also includes many resupinate forms, including some that have traditionally been regarded as heterobasidiomycetes (Sebacinaceae, Tulasnellates, Ceratobasidiales). The euagarics clade, which is by far the largest clade in the Homobasidiomycetes, has the smallest fraction of resupinate species. Results of the present study are compared with recent phylogenetic analyses, and a table summarising the phylogenetic distribution of resupinate taxa is presented, as well as notes on the ecology of resupinate forms and related Homobasidiomycetes.}, author = {Binder, M. and Hibbett, D. S. and Larsson, K. H. and Larsson, E. and Langer, E. and Langer, G.}, interhash = {35bd7f6066d30b80cb445969c9aa3ae4}, intrahash = {a22933b7525f34cc68071d25347e4519}, journal = {Systematics and Biodiversity}, month = jun, number = 2, pages = {113-157}, title = {The phylogenetic distribution of resupinate forms across the major clades of mushroom-forming fungi (Homobasidiomycetes)}, url = {/brokenurl#://000231684600001}, volume = 3, year = 2005 } @misc{yu2013largescale, abstract = {The multi-label classification problem has generated significant interest in recent years. However, existing approaches do not adequately address two key challenges: (a) the ability to tackle problems with a large number (say millions) of labels, and (b) the ability to handle data with missing labels. In this paper, we directly address both these problems by studying the multi-label problem in a generic empirical risk minimization (ERM) framework. Our framework, despite being simple, is surprisingly able to encompass several recent label-compression based methods which can be derived as special cases of our method. To optimize the ERM problem, we develop techniques that exploit the structure of specific loss functions - such as the squared loss function - to offer efficient algorithms. We further show that our learning framework admits formal excess risk bounds even in the presence of missing labels. Our risk bounds are tight and demonstrate better generalization performance for low-rank promoting trace-norm regularization when compared to (rank insensitive) Frobenius norm regularization. Finally, we present extensive empirical results on a variety of benchmark datasets and show that our methods perform significantly better than existing label compression based methods and can scale up to very large datasets such as the Wikipedia dataset.}, author = {Yu, Hsiang-Fu and Jain, Prateek and Kar, Purushottam and Dhillon, Inderjit S.}, interhash = {1252173520757338468a68e028494647}, intrahash = {716e5270c1dcb3a1e4eedf9934859021}, note = {cite arxiv:1307.5101}, title = {Large-scale Multi-label Learning with Missing Labels}, url = {http://arxiv.org/abs/1307.5101}, year = 2013 }