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Description and Use of Animal Breeding Data for Large Least Squares Problems
, 1993
"... Some large rectangular matrices used in animal breeding are presented. We describe how to generate these matrices from the data supplied by animal breeders. The matrices are very sparse (3 nonzeros per row) and range between 26 \Theta 20 and 968 652 \Theta 582 694. 1 Introduction With the introduct ..."
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Some large rectangular matrices used in animal breeding are presented. We describe how to generate these matrices from the data supplied by animal breeders. The matrices are very sparse (3 nonzeros per row) and range between 26 \Theta 20 and 968 652 \Theta 582 694. 1 Introduction With the introduction of supercomputers and massively parallel computers both with very large memories, it has become possible to solve extremely large problems. In order to test the performance of new algorithms, various test problems are needed. A good collection for this purpose is in the Harwell-Boeing collection [1]. Here we suggest a problem from an as yet not well known application, namely the estimation of breeding values. The aim of animal breeders has always been to increase the performance of their animals by selection of the parents. A way to do this is to select as parents those animals which show best performance of the traits of interest. The disadvantage of this method lies in the fact that pe...
A robust preconditioner with low memory requirements for large sparse least squares problems
- SIAM J. Sci. Comput
, 2002
"... Abstract. This paper describes a technique for constructing robust preconditioners for the CGLS method applied to the solution oflarge and sparse least squares problems. The algorithm computes an incomplete LDL T factorization of the normal equations matrix without the need to form the normal matrix ..."
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Abstract. This paper describes a technique for constructing robust preconditioners for the CGLS method applied to the solution oflarge and sparse least squares problems. The algorithm computes an incomplete LDL T factorization of the normal equations matrix without the need to form the normal matrix itself. The preconditioner is reliable (pivot breakdowns cannot occur) and has low intermediate storage requirements. Numerical experiments illustrating the performance of the preconditioner are presented. A comparison with incomplete QR preconditioners is also included.
A Robust Preconditioner With Low Memory
"... We describe a technique for constructing robust preconditioners for the CGNR method applied to the solution of large and sparse least squares problems. Our algorithm computes an incomplete LDL factorization of the normal equations matrix without the need to form the normal matrix itself. The prec ..."
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We describe a technique for constructing robust preconditioners for the CGNR method applied to the solution of large and sparse least squares problems. Our algorithm computes an incomplete LDL factorization of the normal equations matrix without the need to form the normal matrix itself. The preconditioner is reliable (pivot breakdowns cannot occur) and has low intermediate storage requirements. Numerical experiments illustrating the performance of the preconditioner are presented.
