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1 - 10 of 68
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Numerically aware orderings for sparse symmetric indefinite linear systems Hogg J., Scott J., Thorne S. ACM Transactions on Mathematical Software 44(2): 1-22, 2017. Type: Article
The LDLT decomposition of a real symmetric matrix where L is lower triangular with unit diagonal and D diagonal except for 2x2 blocks is a challenge when the matrix is...
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Nov 16 2017 |
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On BLAS level-3 implementations of common solvers for (quasi-) triangular generalized Lyapunov equations Köhler M., Saak J. ACM Transactions on Mathematical Software 43(1): 1-23, 2016. Type: Article
Each of the generalized Lyapunov matrix equations can be seen simply as a system of linear equations in the elements of the unknown matrix X. For numerical solutions, however, it is usually kept in its matrix form. T...
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Oct 20 2016 |
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Active subspaces: emerging ideas for dimension reduction in parameter studies Constantine P., SIAM, Philadelphia, PA, 2015. 110 pp. Type: Book (978-1-611973-85-3)
“SIAM Spotlights” is a new series of short books on topics in computational mathematics and scientific computing. The topic here is active subspaces and how they can reduce the dimension of a parameter study. As des...
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May 13 2016 |
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Linear algebra and matrices: topics for a second course Shapiro H., American Mathematical Society, Boston, MA, 2015. 317 pp. Type: Book (978-1-470418-52-6)
In the preface, the author states that this text grew out of two upper-level courses she taught, one in linear algebra and the other in combinatorial matrix theory. She taught both courses from her own notes because she could not find ...
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Dec 23 2015 |
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Iterative methods for linear systems: theory and applications Olshanskii M., Tyrtyshnikov E., SIAM, Philadelphia, PA, 2014. 263 pp. Type: Book (978-1-611973-45-7)
The term “linear systems” in the title refers to equations of the form Ax = b, where x and b are elements of a Euclidean space and
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Feb 25 2015 |
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OSNAP: faster numerical linear algebra algorithms via sparser subspace embeddings Nelson J., Nguyên H. FOCS 2013 (Proceedings of the IEEE 54th Annual Symposium on Foundations of Computer Science,Oct 26-29, 2013) 117-126, 2013. Type: Proceedings
For the solution of very high-dimensional linear algebra problems, much current research involves dimension reduction using norm-approximating projections. The Johnson–Lindenstrauss lemma [1] establishes the existence of projections th...
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May 12 2014 |
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A solution approach based on Benders decomposition for the preventive maintenance scheduling problem of a stochastic large-scale energy system Lusby R., Muller L., Petersen B. Journal of Scheduling 16(6): 605-628, 2013. Type: Article
The 2010 challenge problem from the French Operations Research Society (FORS) required participants to determine a minimum-cost production and maintenance schedule for a group of power plants, leading to a mixed-integer programming pro...
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Feb 21 2014 |
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Level-3 Cholesky factorization routines improve performance of many Cholesky algorithms Gustavson F., Waśniewski J., Dongarra J., Herrero J., Langou J. ACM Transactions on Mathematical Software 39(2): 1-10, 2013. Type: Article
The Cholesky decomposition of a positive definite matrix is the basis for many efficient and numerically accurate algorithms. The usual procedure is a variant of Gaussian elimination without pivoting, but the computation can be reorder...
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May 6 2013 |
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Algorithm 923: efficient numerical computation of the Pfaffian for dense and banded skew-symmetric matrices Wimmer M. ACM Transactions on Mathematical Software 38(4): 1-17, 2012. Type: Article
The Pfaffian of a matrix, like the determinant, is a polynomial in the matrix elements. It is most frequently used in particle physics where the matrix is even-ordered and skew-symmetric, and the determinant is the square of the Pfaffi...
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Oct 30 2012 |
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A simple division-free algorithm for computing determinants Bird R. Information Processing Letters 111(21-22): 1072-1074, 2011. Type: Article
The determinant of a matrix has a long history in mathematics. It is usually discussed along with Cramer’s rule for the solution of systems of linear equations. As late as the 1950s, the evaluation of 2×2 and 3...
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Sep 28 2012 |
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