I. S. Du#, R. G. Grimes, and J. G. Lewis. Sparse matrix test problems. ACM Trans. Math. Softw., 15(1):1--14, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....moves decrease. 3.1 Experimental Results The mapping heuristics are experimented by mapping some test TIG s onto various size meshes. Test TIG s correspond to the undirected sparse graphs associated with the symmetric sparse matrices selected from Harwel Boeing sparse matrix test collection [4]. Weights of the vertices are assumed to be equal to their degrees. These test TIG s are mapped to 8 Theta 8, 8 Theta 16 and 16 Theta 16 2D meshes. Table 1 illustrates the performance result of the KL, SA, general and meshspecific MFA heuristics for the generated mapping problem instances. In ....

Duff, I.S., and Grius, R.G., "Sparse matrix test problems," ACM Trans. on Matematical software, vol. 17, no. 1, pp. 1-14, March 1989.

.... matrices taken from the Harwell Boeing sparse matrix collection, which is a set of standard test matrices arising from a wide range of sources and disciplines of real applications, such as problems in linear system, least squares, dynamic analysis, structural engineering, and astrophysics [6]. Table 1 gives the statistics for applying our algorithms to a large set of the Harwell Boeing sparse matrix collection. Among the test set, the CIRPHYS dataset was used in circuit physics modeling, the ECONAUS dataset came from the discipline of economics modeling, the LANPRO dataset was for ....

Iain S. Duff, Roger G. Grimes, and John G Lewis, Sparse Matrix Test Problems, ACM Trans. Math. Softw. pp.1-14, 15, 1, Mar. 1989.

....problem is discussed. Convergence problems specific to eigenvalue calculations are identified, and a modification to GD that improves robustness for preconditioning is proposed. In section 4, results are presented from several preconditioners applied on matrices from Hatwell Boeing collection [5], and from atomic physics calculations and comparisons of GD with the modified version are performed. The paper concludes with some final remarks. 2 The Generalized Davidson Method Davidson proposed a way of using the diagonal of A to precondition the Lanczos process [2] In electronic structure ....

I.S. Duff, R.G. Grimes, and J.G. Lewis, Sparse Matrix Test Problems, AC'M Trans. Math. Software 15 (1989) 1. 19

....In all three cases, the final residual norms for the reliable implementation are smaller than the ones as obtained by the MATLAB function A b. Example 3. In this case, we have tested the algorithm for BiCG (or CG if symmetric definite) and CGS on the Harwell Boeing collection of sparse matrices [3]. We compare the original implementations, the reliable implementations, and the implementations of Sleijpen and van der Vorst [19] based on their replacement criteria (16) and (18) In Table 1, we give the results for those matrices for which the computed residuals converge to a level smaller ....

I. S. Duff, R. G. Grimes, and J. G. Lewis, Sparse matrix test problems, ACM Trans. Math. Software, 15 (1989), pp. 1--14.

....results. Unfortunately, there are no simple rules guiding how these factors should be optimized. After the term reduction, we further applies global log entropy weighting [11] to the term frequencies. The resultant term document matrix is stored in a file in the sparse Harwell Boeing format [5]. Finally, the SVD process is invoked against the matrix. The output of the SVD process includes the term matrix T, the document matrix D, and the singular value matrix S. These matrices are saved in files on the disk. For multilingual applications, we require parallel corpora for the training ....

I. Duff and R. Grimes amd J. Lewis. Sparse matrix test problems. A CM 7kans. on Mathematical Software, 15(1), 1989.

....structures works in practice, we consider storing the following sparse matrix: # # # # 3 4 5 6 7 8 9 10 # # # # (3.1) COL: The compressed column format is the most commonly used sparse matrix type in the literature. It is the format chosen for the Harwell Boeing matrix collection [11], and is used in production codes such as SuperLU [10] In this data structure, the nonzeros are arranged by column in a single double precision array: ACOL = 1, 3, 2, 4, 7, 11, 5, 8, 9, 12, 6, 10, 13] The indices of A (often referred to as pointers) corresponding to the first entry in each ....

....is the most commonly used sparse matrix type in the literature. It is the format chosen for the Harwell Boeing matrix collection [11] and is used in production codes such as SuperLU [10] In this data structure, the nonzeros are arranged by column in a single double precision array: ACOL = [1, 3, 2, 4, 7, 11, 5, 8, 9, 12, 6, 10, 13] . The indices of A (often referred to as pointers) corresponding to the first entry in each column is then stored in an integer array: IACOL = 1, 3, 7, 9, 11, 14] The length of the array IA is always one greater than the number of columns, with the last entry is equal to the number of ....

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I. S. Duff, R. G. Grimes, and J. G. Lewis, Sparse matrix test problems, ACM Trans. Math. Softw., 15 (1989), pp. 1--14.

....In all three cases, the final residual norms for the reliable implementation are smaller than the ones as obtained by the MATLAB function Anb. Example 3: In this case, we have tested the algorithm for Bi CG (or CG if symmetric definite) and CGS, on the Harwell Boeing collection of sparse matrices [3]. We compare the original implementations, the reliable implementations and the implementations of Sleijpen and van der Vorst [18] based on their replacement criteria (16) and (18) In Table 1, we give the results for those matrices for which the computed residuals converge to a level smaller ....

I. S. Duff, R. G. Grimes, and J. G. Lewis, Sparse Matrix Test Problems, ACM Trans. Math. Softw., 15 (1989), pp.1-14.

....structures works in practice, we consider storing the following sparse matrix: # # # # 3 4 5 6 7 8 9 10 # # # # (3.1) COL: The compressed column format is the most comonly used sparse matrix type in the literature. It is the format chosen for the Harwell Boeing matrix collection[9], and is used in production codes such as SuperLU[8] In this data structure, the nonzeros are arranged by colmun in a single double precision array: ACOL = 1, 3, 2, 4, 7, 11, 5, 8, 9, 12, 6, 10, 13] The indices of A (often refered to as pointers) corresponding to the first entry in each ....

....format is the most comonly used sparse matrix type in the literature. It is the format chosen for the Harwell Boeing matrix collection[9] and is used in production codes such as SuperLU[8] In this data structure, the nonzeros are arranged by colmun in a single double precision array: ACOL = [1, 3, 2, 4, 7, 11, 5, 8, 9, 12, 6, 10, 13] . The indices of A (often refered to as pointers) corresponding to the first entry in each column is then stored in an integer array: IACOL = 1, 3, 7, 9, 11, 14] The length of the array IA is always one greater than the number of columns, with the last entry is equal to the number of ....

[Article contains additional citation context not shown here]

I. S. Duff, R. G. Grimes, and J. G. Lewis, Sparse matrix test problems, ACM Trans. Math. Softw., 15 (1989), pp. 1--14.

....rather special, class of problems. It is not clear to what extent, if any, those observations can be applied to other problems. For this reason, we discuss additional experiments performed on a selection of nonsymmetric matrices from various sources, including the Harwell Boeing collection [19] and Saad s SPARSKIT [40] These matrices arise from di#erent application areas: oil reservoir modeling, plasma physics, neutron di#usion, metal forming simulation, etc. Some of these matrices arise from finite element modeling, and they have a much more complicated structure than those of the ....

I. S. Duff, R. G. Grimes, and J. G. Lewis, Sparse matrix test problems, ACM Trans. Math. Software, 15 (1989), pp. 1--14.

....tests in matlab versions 4.2a and 4.2c. Throughout the paper, simple matlab notations are used, which the reader is assumed to be familiar with. Table 1 shows the test matrices we use for our numerical experiments. Some of the matrices are from the Harwell Boeing collection (Duff, Grimes and Lewis [5]) The others are artificially made by concatenating two Harwell Boeing matrices. The matrices that are marked with an asterisk do not have the assumed Strong Hall Property, explained in Section 2. Matrix m n nnz Description ABB313 313 176 1557 Sudan Survey data ASH219 219 85 438 Geodesy ....

I. S. Duff, R. G. Grimes, and J. G. Lewis, Sparse matrix test problems, ACM Trans. Math. Softw., 15 (1989), pp. 1--14.

.... their correspondent dual graphs (grid2 dual, airfoil1 dual, 3elt dual, ukerbe1 dual, whitaker3 dual, crack dual and big dual) ffl five De Bruijn networks (DEBR12, DEBR13, DEBR14, DEBR15, DEBR16) ffl two sparse symmetric matrices from the Harwell Gamma Boeing collection (bsspwr09, bcsstk13) [7] plus another sparse matrix from the Nasa collection (nasa4704) ffl four random graphs (G1000:01; G1000:02; U1000:20; U1000:40) The finite elements meshes and the Harwell Boeing graphs have been widely used for evaluating and comparing the performance of several partitioning methods. The De ....

I.S. Duff, R.G.G. Grimmes, and J.G. Lewis, "Sparse Matrix Test Problems," ACM Trans. on Math. Software 15(1), pp. 1-14, 1989.

.... (for real numbers and intervals) Lor71, Bre78, Sas79, Bre80, Bre81, Hul85, Kru86, Abe88, Abe91, Ely90, Ely91, Rat91, Moo91a, Kra88b, Shi89, Wal90a, Kra92b, Kra93c, Loh93] determination of properties of arithmetic [Kah83, Cod88a] comparison of IEEE coprocessors [Juf93] test matrices [Gre69, Duf89] ffl Standard functions with maximum accuracy: Wol80, Wol83a, Wol84, Kra84, Kra86, Bra85, Wol85, Bra86, Bra87, Bra87a, Bra88, Bra90, Kra87, Kra88, Kra90, Kra92, Kra93a, Kra93b, Sch90f] square root [Kah80] complex polynomials [Kra91c] see also: verification methods) computation of ....

Duff, I.S.; Grimes, R.; Lewis, J.: Sparse Matrix Test Problems. ACM Trans. on Math. Software 15(1), 1-14, 1989.

....residual norm is better than with the three term recurrence version of QMR used here; see [13] To emphasize the robustness of the new FQMR method, we ran FQMR on two matrices whose structure is di#erent from the previous examples. These are the Sherman1 matrix and the Sherman5 matrix from [8]. They are the first and fifth matrices from the Sherman collection, respectively. Both represent oil reservoir simulations, with Sherman1 coming from a black oil simulation with shale barriers on a 10 1010 grid with one unknown per grid point, and Sherman5 coming from a fully implicit black oil ....

I. S. Duff, R. G. Grimes, and J. G. Lewis, Sparse matrix test problems, ACM Trans. Math. Software, 15 (1989), pp. 1--14.

....occurrence hash table, and reassign word ids. with their ids and total frequencies. the correct word ids, and output the Figure 1.1. Outline of the preprocessing algorithm a highly sparse word by document matrix. We store this sparse matrix by using the Compressed Column Storage(CCS) format [DGL89] In this format, we record the value of each non zero element, along with its row and column index. The column indices represent the input documents, the row indices represent ids of distinct words present in the document collection, and the non zero entries in the matrix represent the ....

I. Du, R. Grimes, and J. Lewis. Sparse matrix test problems. ACM Trans Math Soft, pages 1-14, 1989.

....in order to avoid an excessive interprocessor traffic computation ratio. 5 Evaluation We implemented the parallel algorithm on the Fujitsu AP1000 and the CRAY T3D and T3E multicomputers, measuring the execution time in meshes of different sizes, using matrices from the Harwell Boeing collection [5, 6]. We also implemented the parallel algorithm using the message passing library of the AP1000 (CellOS) and the MPI standard library. In the results we present, we employed three matrices: BCSPWR10, BCSSTK18 and BCSSTK21 (Table 1) Even though these matrices are symmetric, they have been stored ....

Iain S. Duff, Roger G. Grimes, and John G. Lewis. Sparse matrix test problems. ACM Trans. Math. Softw., 15:1--14, 1989.

....(a) Factorization time. b) Speedup. 4. Results and discussion We implemented the parallel algorithm on the CRAY T3E multicomputer, measuring the execution time in meshes of different sizes, using matrices from the Harwell Boeing Collection and the University of Florida Sparse Matrix Collection [4,2]. A brief description of the main characteristics of the matrices employed is shown in Table 1. Both symmetric and non symmetric matrices have been tested. The number of levels represents the number of sequential steps required in the factorization of the preconditioner. If this number is small ....

I. S. Duff, R. G. Grimes, and J. G. Lewis. Sparse matrix test problems. ACM Trans. Math. Softw., 15:1--14, 1989.

....in order to avoid an excessive interprocessor traffic computation ratio. 3 Evaluation We implemented the parallel algorithm on the Fujitsu AP1000 and the CRAY T3D and T3E multicomputers, measuring the execution time in meshes of different sizes, using matrices from the Harwell Boeing collection [6,7]. We implemented the parallel algorithm using the MPI standard library. In the results we present, three matrices have been employed: BCSPWR10, BCSSTK18 and BCSSTK21 (Table 1) Even though these matrices are symmetric, they have been stored whole, since our objective is to find a general ....

Iain S. Duff, Roger G. Grimes, and John G. Lewis. Sparse matrix test problems. ACM Trans. Math. Softw., 15:1--14, 1989.

....results We tested our colamd ordering algorithm with three sets of matrices: square nonsymmetric matrices, rectangular matrices, and symmetric positive de nite matrices. Our test set is the entire University of Florida sparse matrix collection [7] which includes the Harwell Boeing test set [15, 16], the linear programming problems in Netlib at http: www.netlib.org [13] as well as many other matrices. We exclude complex matrices, nonsymmetric matrices for which only the pattern was provided, and unassembled nite element matrices. Some matrices include explicit zero entries in the ....

I. S. Du, R. G. Grimes, and J. G. Lewis. Sparse matrix test problems. ACM Trans. Math. Softw., 15:1-14, 1989.

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Duff, I. S., Grimes, R. G., and Lewis, J. G. Sparse matrix test problems. ACM Trans. Math. Softw., 15:1--14, 1989.

....6. Performance results. In this section, we present the results of our experiments with AMD on a wide range of test matrices. We first show that if we replace APPROXIMATE MINIMUM DEGREE 13 Table 1 Matrices in test set Source number classification, and comments or discipline Harwell Boeing see [8, 7] for disciplines 7 PUA (pattern only, unsymmetric, assembled) 93 RUA (real, unsymmetric, assembled) 89 PSA (pattern only, symmetric, assembled) 49 RSA (real, symmetric, assembled) SPARSKIT2: computational fluid dynamics FIDAP 35 RUA, regular 2D and 3D grids Tokamak 4 RUA (but with symmetric ....

....well known ordering codes. 6.1. Test Matrices. Our test set consists of 318 matrices, ranging in size from 9by 9 to 76480 by 76480. All matrices are available via anonymous ftp. We included all non dense and non diagonal matrices from the Harwell Boeing collection of type PUA, RUA, PSA, and RSA [7, 8] (at orion.cerfacs.fr or numerical.cc.rl.ac.uk) thus excluding only 19 matrices from this collection. We also included Saad s SPARSKIT2 collection (at ftp.cs.umn.edu) and the collection at the University of Florida (available from ftp.cis.ufl.edu in the directory pub umfpack matrices) For the ....

I. S. Duff, R. G. Grimes, and J. G. Lewis, Sparse matrix test problems, ACM Trans. Math. Softw., 15 (1989), pp. 1--14.

....in Section 4.1 and illustrate problems that can occur when we try to detect ill conditioning from the factored form. We show the reliability of our incremental norm estimator in Section 5, by presenting results obtained from a variety of dense and sparse test cases from standard matrix collections (Duff, Grimes and Lewis 1989, Higham 1995) Finally, we give our conclusions in Section 6. 2 Incremental estimators In this section, we present the details of our incremental norm estimator. The principal conceptual difference between our scheme and the original incremental condition estimator (ICE) Bischof 1990) is that ....

....with dense and sparse matrices. We use the algorithm described in Section 3.1 which allows us to use our norm estimator on both the triangular factor and its inverse. In Table 5. 1, we show the incremental estimates for the QR factorization of sparse matrices from the Harwell Boeing collection (Duff et al. 1989). Here, the second column displays the exact matrix norm of R as calculated by MATLAB, the third and fourth columns show estimations based on approximate left singular vectors and on approximate right singular vectors, respectively. In general, both of our estimators give a good approximation to ....

Duff, I. S., Grimes, R. G. and Lewis, J. G. (1989), `Sparse matrix test problems', ACM Trans. Math. Softw. 15(1), 1--14.

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I. S. Du#, R. G. Grimes, and J. G. Lewis. Sparse matrix test problems. ACM Trans. Math. Softw., 15(1):1--14, 1989.

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I.S. Duff, R.G. Grimes, and J.G. Lewis. Sparse matrix test problems. ACM Trans. Math. Software, 15:1--14, 1989.

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I. S. Duff, R. G. Grimes, and J. G. Lewis, Sparse matrix test problems, ACM Trans. Math. Softw., 15 (1989), pp. 1--14.

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Duff, I. S., Grimes, R. G., and Lewis, J. G. Sparse matrix test problems. ACM Trans. Math. Software 15 (1989), 1--14.

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