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Crawford, Charles
retired
Toronto, Canada
 
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- 10 of 68 reviews

   
  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...

Nov 16 2017  
  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...

Oct 20 2016  
  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...

May 13 2016  
  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 ...

Dec 23 2015  
   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
Feb 25 2015  
  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...

May 12 2014  
  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...

Feb 21 2014  
  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...

May 6 2013  
   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...

Oct 30 2012  
  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&#...

Sep 28 2012  
 
 
 
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