Application of supernodal sparse factorization and inversion to the estimation of (co)variance components by residual maximum likelihood
We demonstrated that supernodal techniques were more efficient than traditional methods for factorization and inversion of a coefficient matrix of mixed model equations (MME), which are often required in residual maximum likelihood (REML). Supernodal left‐looking and inverse multifrontal algorithms...
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| Veröffentlicht in: | Journal of animal breeding and genetics (1986) Jg. 131; H. 3; S. 227 - 236 |
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Blackwell Wissenschafts-Verlag
01.06.2014
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| Abstract | We demonstrated that supernodal techniques were more efficient than traditional methods for factorization and inversion of a coefficient matrix of mixed model equations (MME), which are often required in residual maximum likelihood (REML). Supernodal left‐looking and inverse multifrontal algorithms were employed for sparse factorization and inversion, respectively. The approximate minimum degree or multilevel nested dissection was used for ordering. A new computer package, Yet Another MME Solver (yams), was developed and compared with fspak with respect to computing time and size of temporary memory for 13 test matrices. The matrices were produced by fitting animal models to dairy data and by using simulations from sire, sire–maternal grand sire, maternal and dominance models for phenotypic data and animal model for genomic data. The order of matrices ranged from 32 840 to 1 048 872. The yams software factorized and inverted the matrices up to 13 and 10 times faster than fspak, respectively, when an appropriate ordering strategy was applied. The yams package required at most 282 MB and 512 MB of temporary memory for factorization and inversion, respectively. Processing time per iteration in average information REML was reduced, using yams. The yams package is freely available on request by contacting the corresponding author. |
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| AbstractList | We demonstrated that supernodal techniques were more efficient than traditional methods for factorization and inversion of a coefficient matrix of mixed model equations (MME), which are often required in residual maximum likelihood (REML). Supernodal left-looking and inverse multifrontal algorithms were employed for sparse factorization and inversion, respectively. The approximate minimum degree or multilevel nested dissection was used for ordering. A new computer package, Yet Another MME Solver (YAMS), was developed and compared with FSPAK with respect to computing time and size of temporary memory for 13 test matrices. The matrices were produced by fitting animal models to dairy data and by using simulations from sire, sire-maternal grand sire, maternal and dominance models for phenotypic data and animal model for genomic data. The order of matrices ranged from 32,840 to 1,048,872. The YAMS software factorized and inverted the matrices up to 13 and 10 times faster than FSPAK, respectively, when an appropriate ordering strategy was applied. The YAMS package required at most 282 MB and 512 MB of temporary memory for factorization and inversion, respectively. Processing time per iteration in average information REML was reduced, using YAMS. The YAMS package is freely available on request by contacting the corresponding author. We demonstrated that supernodal techniques were more efficient than traditional methods for factorization and inversion of a coefficient matrix of mixed model equations ( MME ), which are often required in residual maximum likelihood ( REML ). Supernodal left‐looking and inverse multifrontal algorithms were employed for sparse factorization and inversion, respectively. The approximate minimum degree or multilevel nested dissection was used for ordering. A new computer package, Yet Another MME Solver ( yams ), was developed and compared with fspak with respect to computing time and size of temporary memory for 13 test matrices. The matrices were produced by fitting animal models to dairy data and by using simulations from sire, sire–maternal grand sire, maternal and dominance models for phenotypic data and animal model for genomic data. The order of matrices ranged from 32 840 to 1 048 872. The yams software factorized and inverted the matrices up to 13 and 10 times faster than fspak , respectively, when an appropriate ordering strategy was applied. The yams package required at most 282 MB and 512 MB of temporary memory for factorization and inversion, respectively. Processing time per iteration in average information REML was reduced, using yams . The yams package is freely available on request by contacting the corresponding author. We demonstrated that supernodal techniques were more efficient than traditional methods for factorization and inversion of a coefficient matrix of mixed model equations (MME), which are often required in residual maximum likelihood (REML). Supernodal left-looking and inverse multifrontal algorithms were employed for sparse factorization and inversion, respectively. The approximate minimum degree or multilevel nested dissection was used for ordering. A new computer package, Yet Another MME Solver (YAMS), was developed and compared with FSPAK with respect to computing time and size of temporary memory for 13 test matrices. The matrices were produced by fitting animal models to dairy data and by using simulations from sire, sire-maternal grand sire, maternal and dominance models for phenotypic data and animal model for genomic data. The order of matrices ranged from 32,840 to 1,048,872. The YAMS software factorized and inverted the matrices up to 13 and 10 times faster than FSPAK, respectively, when an appropriate ordering strategy was applied. The YAMS package required at most 282 MB and 512 MB of temporary memory for factorization and inversion, respectively. Processing time per iteration in average information REML was reduced, using YAMS. The YAMS package is freely available on request by contacting the corresponding author.We demonstrated that supernodal techniques were more efficient than traditional methods for factorization and inversion of a coefficient matrix of mixed model equations (MME), which are often required in residual maximum likelihood (REML). Supernodal left-looking and inverse multifrontal algorithms were employed for sparse factorization and inversion, respectively. The approximate minimum degree or multilevel nested dissection was used for ordering. A new computer package, Yet Another MME Solver (YAMS), was developed and compared with FSPAK with respect to computing time and size of temporary memory for 13 test matrices. The matrices were produced by fitting animal models to dairy data and by using simulations from sire, sire-maternal grand sire, maternal and dominance models for phenotypic data and animal model for genomic data. The order of matrices ranged from 32,840 to 1,048,872. The YAMS software factorized and inverted the matrices up to 13 and 10 times faster than FSPAK, respectively, when an appropriate ordering strategy was applied. The YAMS package required at most 282 MB and 512 MB of temporary memory for factorization and inversion, respectively. Processing time per iteration in average information REML was reduced, using YAMS. The YAMS package is freely available on request by contacting the corresponding author. Summary We demonstrated that supernodal techniques were more efficient than traditional methods for factorization and inversion of a coefficient matrix of mixed model equations (MME), which are often required in residual maximum likelihood (REML). Supernodal left‐looking and inverse multifrontal algorithms were employed for sparse factorization and inversion, respectively. The approximate minimum degree or multilevel nested dissection was used for ordering. A new computer package, Yet Another MME Solver (yams), was developed and compared with fspak with respect to computing time and size of temporary memory for 13 test matrices. The matrices were produced by fitting animal models to dairy data and by using simulations from sire, sire–maternal grand sire, maternal and dominance models for phenotypic data and animal model for genomic data. The order of matrices ranged from 32 840 to 1 048 872. The yams software factorized and inverted the matrices up to 13 and 10 times faster than fspak, respectively, when an appropriate ordering strategy was applied. The yams package required at most 282 MB and 512 MB of temporary memory for factorization and inversion, respectively. Processing time per iteration in average information REML was reduced, using yams. The yams package is freely available on request by contacting the corresponding author. Summary We demonstrated that supernodal techniques were more efficient than traditional methods for factorization and inversion of a coefficient matrix of mixed model equations (MME), which are often required in residual maximum likelihood (REML). Supernodal left-looking and inverse multifrontal algorithms were employed for sparse factorization and inversion, respectively. The approximate minimum degree or multilevel nested dissection was used for ordering. A new computer package, Yet Another MME Solver (yams), was developed and compared with fspak with respect to computing time and size of temporary memory for 13 test matrices. The matrices were produced by fitting animal models to dairy data and by using simulations from sire, sire-maternal grand sire, maternal and dominance models for phenotypic data and animal model for genomic data. The order of matrices ranged from 32 840 to 1 048 872. The yams software factorized and inverted the matrices up to 13 and 10 times faster than fspak, respectively, when an appropriate ordering strategy was applied. The yams package required at most 282 MB and 512 MB of temporary memory for factorization and inversion, respectively. Processing time per iteration in average information REML was reduced, using yams. The yams package is freely available on request by contacting the corresponding author. [PUBLICATION ABSTRACT] |
| Author | Baba, T. Suzuki, M. Masuda, Y. |
| Author_xml | – sequence: 1 fullname: Masuda, Y – sequence: 2 fullname: Baba, T – sequence: 3 fullname: Suzuki, M |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/24906028$$D View this record in MEDLINE/PubMed |
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| Cites_doi | 10.1111/j.1439-0388.2008.00774.x 10.1137/S0895479894278952 10.1137/0914048 10.1145/1916461.1916464 10.1080/10618600.1995.10474671 10.1016/j.livsci.2007.04.023 10.1137/S0895479899358194 10.21236/ADA326874 10.1137/S1064827595287997 10.3168/jds.2009-2730 10.1137/1.9780898719604 10.1111/j.1439-0388.1998.tb00347.x 10.1145/1391989.1391995 10.1137/09077432X 10.1137/0914063 10.1145/360680.360704 10.1079/9780851990002.0000 10.1137/1.9780898718881 10.3168/jds.S0022-0302(93)77478-0 10.1145/1377603.1377607 10.1145/1236463.1236465 10.1137/0614019 10.1093/bioinformatics/btp045 |
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| Copyright | 2013 Blackwell Verlag GmbH 2013 Blackwell Verlag GmbH. Copyright © 2014 Blackwell Verlag GmbH |
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| Keywords | residual maximum likelihood sparse matrix mixed model equations Computing methods |
| Language | English |
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| Notes | http://dx.doi.org/10.1111/jbg.12058 Methods S1 Additional comparisons. Results S1 Factorization and inversion. istex:2EA8E397B0FAA4468ECF556E2F8302360DE5B6C3 ArticleID:JBG12058 ark:/67375/WNG-H6XCFBW8-R ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23 ObjectType-Article-2 ObjectType-Feature-1 |
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| References | Mrode R.A. (2005) Linear Models for the Prediction of Animal Breeding Values. CABI Publishing, Oxford, UK. Misztal I., Pérez-Enciso M. (1993) Sparse matrix inversion for restricted maximum likelihood estimation of variance components by expectation-maximization. J. Dairy Sci., 76, 1479-1483. Sargolzaei M., Schenkel F.S. (2009) QMSim: a large-scale genome simulator for livestock. Bioinformatics, 25, 680-681. Togashi K., Lin C.Y., Atagi Y., Hagiya K., Sato J., Nakanishi T. (2008) Genetic characteristics of Japanese Holstein cows based on multiple-lactation random regression test-day animal models. Livest. Sci., 114, 194-201. Erisman A.M., Tinney W.F. (1975) On computing certain elements of the inverse of a sparse matrix. Commun. ACM, 18, 177-179. Misztal I. (2008) Reliable computing in estimation of variance components. J. Anim. Breed. Genet., 125, 363-370. Anderson E., Bai Z., Bischof C., Blackford S., Demmel J., Dongarra J., Du Croz J., Greenbaum A., Hammarling S., McKenney A., Sorensen D. (1999) LAPACK Users' Guide, 3rd edn. Society for Industrial and Applied Mathematics, Philadelphia, PA. Ng E.G., Peyton B.W. (1993b) Block sparse Cholesky algorithms on advanced uniprocessor computers. SIAM J. Sci. Comp., 14, 1034-1056. Karypis G., Kumar V. (1998) A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comp., 20, 359-392. Aguilar I., Misztal I., Johnson D.L., Legarra A., Tsuruta S., Lawlor T.J. (2010) Hot topic: a unified approach to utilize phenotypic, full pedigree, and genomic information for genetic evaluation of Holstein final score. J. Dairy Sci., 93, 743-752. Amestoy P.R., Duff I.S., L'Excellent J.-Y., Koster J. (2001) A fully asynchronous multifrontal solver using distributed dynamic scheduling. SIAM J. Matrix Anal. Appl., 23, 15-41. Hofer A. (1998) Variance component estimation in animal breeding: a review. J. Anim. Breed. Genet., 115, 247-265. Smith S.P. (1995) Differentiation of the Cholesky algorithm. J. Comput. Graph. Stat., 4, 134-147. Davis T.A. (2006) Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2). Society for Industrial and Applied Mathematics, Philadelphia, PA. Amestoy P.R., Davis T.A., Duff I.S. (1996) An approximate minimum degree ordering algorithm. SIAM J. Matrix Anal. Appl., 17, 886-905. Goto K., Van De Geijn R. (2008) High-performance implementation of the level-3 BLAS. ACM Trans. Math. Softw., 35, 4. Ng E.G., Peyton B.W. (1993a) A supernodal Cholesky factorization algorithm for shared-memory multiprocessors. SIAM J. Sci. Comp., 14, 761-769. Lin L., Yang C., Lu J., Ying L., Weinan E. (2011a) A fast parallel algorithm for selected inversion of structured sparse matrices with application to 2D electronic structure calculations. SIAM J. Sci. Comp., 33, 1329-1351. George A., Liu J.W.H. (1981) Computer Solution of Large Sparse Positive Definite Systems. Prentice Hall Professional Technical Reference, Englewood Cliffs, NJ. Jensen J., Mäntysaari E.A., Madsen P., Thompson R. (1997) Residual maximum likelihood estimation of (co)variance components in multivariate mixed linear models using average information. J. Indian Soc. Agric. Stat., 49, 215-236. Lin L., Yang C., Meza J.C., Lu J., Ying L. (2011b) SelInv - an algorithm for selected inversion of a sparse symmetric matrix. ACM Trans. Math. Softw., 37, 40. Chen Y., Davis T.A., Hager W.W., Rajamanickam S. (2008) Algorithm 887: CHOLMOD, supernodal sparse Cholesky factorization and update/downdate. ACM Trans. Math. Softw., 35, 22. Liu J.W.H., Ng E.G., Peyton B.W. (1993) On finding supernodes for sparse matrix computations. SIAM J. Matrix Anal. Appl., 14, 242-252. Boldman K.G., Kriese L.A., Van Vleck L.D., Van Tassell C.P., Kachman S.D. (1995) A Manual for Use of MTDFREML. ARS, USDA, Washington, DC. Gould N.I.M., Scott J.A., Hu Y. (2007) A numerical evaluation of sparse direct solvers for the solution of large sparse symmetric linear systems of equations. ACM Trans. Math. Softw., 33, 10. 2009; 25 1996; 17 1993b; 14 1975; 18 1995 2008; 35 2006 1997; 49 1998; 115 2005 1994 2008; 125 2002 1991 2001; 23 2007; 33 1995; 4 1998; 20 1999 2011a; 33 1993; 14 2011b; 37 1993; 76 1981 2008; 114 2010; 93 1993a; 14 Boldman K.G. (e_1_2_5_6_1) 1995 e_1_2_5_28_1 e_1_2_5_25_1 e_1_2_5_26_1 e_1_2_5_24_1 e_1_2_5_21_1 e_1_2_5_22_1 George A. (e_1_2_5_11_1) 1981 Meyer K. (e_1_2_5_20_1) 2005 e_1_2_5_29_1 Jensen J. (e_1_2_5_15_1) 1997; 49 e_1_2_5_14_1 e_1_2_5_17_1 e_1_2_5_9_1 e_1_2_5_16_1 e_1_2_5_8_1 Smith S.P. (e_1_2_5_30_1) 1995; 4 e_1_2_5_7_1 e_1_2_5_10_1 Pérez‐Enciso M. (e_1_2_5_27_1) 1994 e_1_2_5_5_1 e_1_2_5_12_1 e_1_2_5_4_1 e_1_2_5_3_1 e_1_2_5_2_1 e_1_2_5_19_1 e_1_2_5_18_1 Misztal I. (e_1_2_5_23_1) 2002 e_1_2_5_31_1 Gould N.I.M. (e_1_2_5_13_1) 2007; 33 |
| References_xml | – reference: Goto K., Van De Geijn R. (2008) High-performance implementation of the level-3 BLAS. ACM Trans. Math. Softw., 35, 4. – reference: Jensen J., Mäntysaari E.A., Madsen P., Thompson R. (1997) Residual maximum likelihood estimation of (co)variance components in multivariate mixed linear models using average information. J. Indian Soc. Agric. Stat., 49, 215-236. – reference: Gould N.I.M., Scott J.A., Hu Y. (2007) A numerical evaluation of sparse direct solvers for the solution of large sparse symmetric linear systems of equations. ACM Trans. Math. Softw., 33, 10. – reference: Amestoy P.R., Davis T.A., Duff I.S. (1996) An approximate minimum degree ordering algorithm. SIAM J. Matrix Anal. Appl., 17, 886-905. – reference: Amestoy P.R., Duff I.S., L'Excellent J.-Y., Koster J. (2001) A fully asynchronous multifrontal solver using distributed dynamic scheduling. SIAM J. Matrix Anal. Appl., 23, 15-41. – reference: Misztal I. (2008) Reliable computing in estimation of variance components. J. Anim. Breed. Genet., 125, 363-370. – reference: Misztal I., Pérez-Enciso M. (1993) Sparse matrix inversion for restricted maximum likelihood estimation of variance components by expectation-maximization. J. Dairy Sci., 76, 1479-1483. – reference: Lin L., Yang C., Meza J.C., Lu J., Ying L. (2011b) SelInv - an algorithm for selected inversion of a sparse symmetric matrix. ACM Trans. Math. Softw., 37, 40. – reference: Smith S.P. (1995) Differentiation of the Cholesky algorithm. J. Comput. Graph. Stat., 4, 134-147. – reference: George A., Liu J.W.H. (1981) Computer Solution of Large Sparse Positive Definite Systems. Prentice Hall Professional Technical Reference, Englewood Cliffs, NJ. – reference: Togashi K., Lin C.Y., Atagi Y., Hagiya K., Sato J., Nakanishi T. (2008) Genetic characteristics of Japanese Holstein cows based on multiple-lactation random regression test-day animal models. Livest. Sci., 114, 194-201. – reference: Chen Y., Davis T.A., Hager W.W., Rajamanickam S. (2008) Algorithm 887: CHOLMOD, supernodal sparse Cholesky factorization and update/downdate. ACM Trans. Math. Softw., 35, 22. – reference: Erisman A.M., Tinney W.F. (1975) On computing certain elements of the inverse of a sparse matrix. Commun. ACM, 18, 177-179. – reference: Liu J.W.H., Ng E.G., Peyton B.W. (1993) On finding supernodes for sparse matrix computations. SIAM J. Matrix Anal. Appl., 14, 242-252. – reference: Anderson E., Bai Z., Bischof C., Blackford S., Demmel J., Dongarra J., Du Croz J., Greenbaum A., Hammarling S., McKenney A., Sorensen D. (1999) LAPACK Users' Guide, 3rd edn. Society for Industrial and Applied Mathematics, Philadelphia, PA. – reference: Ng E.G., Peyton B.W. (1993b) Block sparse Cholesky algorithms on advanced uniprocessor computers. SIAM J. Sci. Comp., 14, 1034-1056. – reference: Ng E.G., Peyton B.W. (1993a) A supernodal Cholesky factorization algorithm for shared-memory multiprocessors. SIAM J. Sci. Comp., 14, 761-769. – reference: Lin L., Yang C., Lu J., Ying L., Weinan E. (2011a) A fast parallel algorithm for selected inversion of structured sparse matrices with application to 2D electronic structure calculations. SIAM J. Sci. Comp., 33, 1329-1351. – reference: Boldman K.G., Kriese L.A., Van Vleck L.D., Van Tassell C.P., Kachman S.D. (1995) A Manual for Use of MTDFREML. ARS, USDA, Washington, DC. – reference: Karypis G., Kumar V. (1998) A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comp., 20, 359-392. – reference: Mrode R.A. (2005) Linear Models for the Prediction of Animal Breeding Values. CABI Publishing, Oxford, UK. – reference: Aguilar I., Misztal I., Johnson D.L., Legarra A., Tsuruta S., Lawlor T.J. (2010) Hot topic: a unified approach to utilize phenotypic, full pedigree, and genomic information for genetic evaluation of Holstein final score. J. Dairy Sci., 93, 743-752. – reference: Davis T.A. (2006) Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2). Society for Industrial and Applied Mathematics, Philadelphia, PA. – reference: Hofer A. (1998) Variance component estimation in animal breeding: a review. J. Anim. Breed. Genet., 115, 247-265. – reference: Sargolzaei M., Schenkel F.S. (2009) QMSim: a large-scale genome simulator for livestock. Bioinformatics, 25, 680-681. – volume: 35 start-page: 4 year: 2008 article-title: High‐performance implementation of the level‐3 BLAS publication-title: ACM Trans. Math. Softw. – start-page: 87 year: 1994 end-page: 88 – year: 1981 – volume: 49 start-page: 215 year: 1997 end-page: 236 article-title: Residual maximum likelihood estimation of (co)variance components in multivariate mixed linear models using average information publication-title: J. Indian Soc. Agric. Stat. – volume: 18 start-page: 177 year: 1975 end-page: 179 article-title: On computing certain elements of the inverse of a sparse matrix publication-title: Commun. ACM – year: 2005 – volume: 33 start-page: 10 year: 2007 article-title: A numerical evaluation of sparse direct solvers for the solution of large sparse symmetric linear systems of equations publication-title: ACM Trans. Math. Softw. – volume: 37 start-page: 40 year: 2011b article-title: SelInv – an algorithm for selected inversion of a sparse symmetric matrix publication-title: ACM Trans. Math. Softw. – volume: 4 start-page: 134 year: 1995 end-page: 147 article-title: Differentiation of the Cholesky algorithm publication-title: J. Comput. Graph. Stat. – volume: 17 start-page: 886 year: 1996 end-page: 905 article-title: An approximate minimum degree ordering algorithm publication-title: SIAM J. Matrix Anal. Appl. – volume: 125 start-page: 363 year: 2008 end-page: 370 article-title: Reliable computing in estimation of variance components publication-title: J. Anim. Breed. Genet. – volume: 20 start-page: 359 year: 1998 end-page: 392 article-title: A fast and high quality multilevel scheme for partitioning irregular graphs publication-title: SIAM J. Sci. Comp. – volume: 114 start-page: 194 year: 2008 end-page: 201 article-title: Genetic characteristics of Japanese Holstein cows based on multiple‐lactation random regression test‐day animal models publication-title: Livest. Sci. – volume: 14 start-page: 1034 year: 1993b end-page: 1056 article-title: Block sparse Cholesky algorithms on advanced uniprocessor computers publication-title: SIAM J. Sci. Comp. – volume: 33 start-page: 1329 year: 2011a end-page: 1351 article-title: A fast parallel algorithm for selected inversion of structured sparse matrices with application to 2D electronic structure calculations publication-title: SIAM J. Sci. Comp. – volume: 14 start-page: 761 year: 1993a end-page: 769 article-title: A supernodal Cholesky factorization algorithm for shared‐memory multiprocessors publication-title: SIAM J. Sci. Comp. – year: 2002 – year: 2006 – volume: 35 start-page: 22 year: 2008 article-title: Algorithm 887: CHOLMOD, supernodal sparse Cholesky factorization and update/downdate publication-title: ACM Trans. Math. Softw. – volume: 14 start-page: 242 year: 1993 end-page: 252 article-title: On finding supernodes for sparse matrix computations publication-title: SIAM J. Matrix Anal. Appl. – year: 1995 – start-page: 282 year: 2005 end-page: 285 – volume: 25 start-page: 680 year: 2009 end-page: 681 article-title: QMSim: a large‐scale genome simulator for livestock publication-title: Bioinformatics – volume: 115 start-page: 247 year: 1998 end-page: 265 article-title: Variance component estimation in animal breeding: a review publication-title: J. Anim. Breed. Genet. – volume: 76 start-page: 1479 year: 1993 end-page: 1483 article-title: Sparse matrix inversion for restricted maximum likelihood estimation of variance components by expectation‐maximization publication-title: J. Dairy Sci. – year: 1991 – volume: 93 start-page: 743 year: 2010 end-page: 752 article-title: Hot topic: a unified approach to utilize phenotypic, full pedigree, and genomic information for genetic evaluation of Holstein final score publication-title: J. Dairy Sci. – volume: 23 start-page: 15 year: 2001 end-page: 41 article-title: A fully asynchronous multifrontal solver using distributed dynamic scheduling publication-title: SIAM J. Matrix Anal. Appl. – year: 1999 – ident: e_1_2_5_21_1 doi: 10.1111/j.1439-0388.2008.00774.x – ident: e_1_2_5_3_1 doi: 10.1137/S0895479894278952 – ident: e_1_2_5_25_1 doi: 10.1137/0914048 – start-page: 87 volume-title: Proceedings of the 5th World Congress on Genetics Applied to Livestock Production year: 1994 ident: e_1_2_5_27_1 – ident: e_1_2_5_18_1 doi: 10.1145/1916461.1916464 – volume: 4 start-page: 134 year: 1995 ident: e_1_2_5_30_1 article-title: Differentiation of the Cholesky algorithm publication-title: J. Comput. Graph. Stat. doi: 10.1080/10618600.1995.10474671 – ident: e_1_2_5_31_1 doi: 10.1016/j.livsci.2007.04.023 – ident: e_1_2_5_4_1 doi: 10.1137/S0895479899358194 – volume: 49 start-page: 215 year: 1997 ident: e_1_2_5_15_1 article-title: Residual maximum likelihood estimation of (co)variance components in multivariate mixed linear models using average information publication-title: J. Indian Soc. Agric. Stat. – ident: e_1_2_5_28_1 doi: 10.21236/ADA326874 – ident: e_1_2_5_7_1 – ident: e_1_2_5_16_1 doi: 10.1137/S1064827595287997 – start-page: 282 volume-title: Proceedings of the 16th Conference of the Association for the Advancement of Animal Breeding and Genetics year: 2005 ident: e_1_2_5_20_1 – ident: e_1_2_5_2_1 doi: 10.3168/jds.2009-2730 – ident: e_1_2_5_5_1 doi: 10.1137/1.9780898719604 – ident: e_1_2_5_14_1 doi: 10.1111/j.1439-0388.1998.tb00347.x – ident: e_1_2_5_8_1 doi: 10.1145/1391989.1391995 – ident: e_1_2_5_17_1 doi: 10.1137/09077432X – ident: e_1_2_5_26_1 doi: 10.1137/0914063 – ident: e_1_2_5_10_1 doi: 10.1145/360680.360704 – ident: e_1_2_5_24_1 doi: 10.1079/9780851990002.0000 – ident: e_1_2_5_9_1 doi: 10.1137/1.9780898718881 – volume-title: Proceedings of the 7th World Congress on Genetics Applied to Livestock Production year: 2002 ident: e_1_2_5_23_1 – volume-title: Computer Solution of Large Sparse Positive Definite Systems year: 1981 ident: e_1_2_5_11_1 – ident: e_1_2_5_22_1 doi: 10.3168/jds.S0022-0302(93)77478-0 – ident: e_1_2_5_12_1 doi: 10.1145/1377603.1377607 – volume: 33 start-page: 10 year: 2007 ident: e_1_2_5_13_1 article-title: A numerical evaluation of sparse direct solvers for the solution of large sparse symmetric linear systems of equations publication-title: ACM Trans. Math. Softw. doi: 10.1145/1236463.1236465 – ident: e_1_2_5_19_1 doi: 10.1137/0614019 – volume-title: A Manual for Use of MTDFREML year: 1995 ident: e_1_2_5_6_1 – ident: e_1_2_5_29_1 doi: 10.1093/bioinformatics/btp045 |
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| Snippet | We demonstrated that supernodal techniques were more efficient than traditional methods for factorization and inversion of a coefficient matrix of mixed model... Summary We demonstrated that supernodal techniques were more efficient than traditional methods for factorization and inversion of a coefficient matrix of... Summary We demonstrated that supernodal techniques were more efficient than traditional methods for factorization and inversion of a coefficient matrix of... |
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| SubjectTerms | Algorithms Analysis of Variance Animal models Animal reproduction Animals Breeding Cattle Computational Biology Computational Biology - methods computer software Computing methods Dairying equations Female Genomics Likelihood Functions Male methods mixed model equations residual maximum likelihood sires Software sparse matrix Statistics as Topic Statistics as Topic - methods Time Factors variance |
| Title | Application of supernodal sparse factorization and inversion to the estimation of (co)variance components by residual maximum likelihood |
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