Linear Algebra

  1. Martin Albrecht, Gregory Bard, and William Hart, Algorithm 898: Efficient multiplication of dense matrices over GF(2), TOMS 37 (2010), no. 1.[doi]
  2. Martin R. Albrecht and Clément Pernet, Efficient decomposition of dense matrices over GF(2), Preprint (2010), 1–17.
  3. Tomas J. Boothby and Robert W. Bradshaw, Bitslicing and the method of four Russians over larger finite fields, preprint (2009), 1–10.[arXiv]
  4. Nigel Boston, Spaces of constant rank matrices over GF(2), Electron. J. Linear Algebra 20 (2010), 1–5.[MR]
  5. Paul-Olivier Dehaye, Joint moments of derivatives of characteristic polynomials, Algebra Number Theory 2 (2008), no. 1, 31–68.[MR]
  6. Jean-Guillaume Dumas, Thierry Gautier, Pascal Giorgi, and Clément Pernet, Dense linear algebra over finite fields: The FFLAS and FFPACK packages, preprint (2006), 69 pages.[arXiv]
  7. Jean-Guillaume Dumas, Pascal Giorgi, and Clément Pernet, FFPACK: finite field linear algebra package, ISSAC '2004: Proceedings of the 2004 International Symposium on Symbolic and Algebraic Computation, ACM, New York, 2004, pp. 119–126.[MR]
  8. Jean-Guillaume Dumas, Pascal Giorgi, and Clément Pernet, Dense linear algebra over word-size prime fields: The FFLAS and FFPACK packages, ACM Trans. Math. Softw. 35 (2008), no. 3, 1–42.[doi]
  9. Jean-Guillaume Dumas, Clément Pernet, and Zhendong Wan, Efficient computation of the characteristic polynomial, ISSAC'05: Proceedings of the 2005 International Symposium on Symbolic and Algebraic Computation, ACM, New York, 2005, pp. 140–147 (electronic).[MR/arXiv]
  10. Jean-Guillaume Dumas and Anna Urbanska, An introspective algorithm for the integer determinant, preprint (2006), 32 pages.[arXiv]
  11. Wayne Eberly, Mark Giesbrecht, Pascal Giorgi, Arne Storjohann, and Gilles Villard, Faster inversion and other black box matrix computations using efficient block projections, ISSAC 2007, ACM, New York, 2007, pp. 143–150.[MR/arXiv]
  12. Cesar A. Garcia-Vazquez and Carlos A. Lopez-Andrade, D-Heaps as hash tables for vectors over a finite ring, 2009 WRI World Conference on Computer Science and Information Engineering, WRI World Congress on Computer Science and Information Engineering, vol. 3, IEEE, 2009, pp. 162–166.[doi]
  13. Katharina Geißler and Nigel P. Smart, Computing the M = UUt integer matrix decomposition, Cryptography and Coding, Lecture Notes in Comput. Sci., vol. 2898, Springer, Berlin, 2003, pp. 223–233.[MR]
  14. George Havas, Derek F. Holt, and Sarah Rees, Recognizing badly presented Z-modules, Linear Algebra Appl. 192 (1993), 137–163.[MR]
  15. George Havas, Bohdan S. Majewski, and Keith R. Matthews, Extended GCD and Hermite normal form algorithms via lattice basis reduction, Experiment. Math. 7 (1998), no. 2, 125–136.[MR]
  16. George Havas, Bohdan S. Majewski, and Keith R. Matthews, Addenda and errata: "Extended GCD and Hermite normal form algorithms via lattice basis reduction", Experiment. Math. 8 (1999), no. 2, 205.[MR]
  17. Gerold Jaeger, Parallel algorithms for computing the Smith normal form of large matrices, Recent Advances in Parallel Virtual Machine and Message Passing Interface, vol. 2840, Springer, Berlin/Heidelberg, 2003, pp. 170–179.
  18. G. Jäger, Reduction of Smith normal form transformation matrices, Computing 74 (2005), no. 4, 377–388.[MR]
  19. Marjeta Kramar, The structure of irreducible matrix groups with submultiplicative spectrum, Linear Multilinear Algebra 53 (2005), no. 1, 13–25.[MR]
  20. R. V. Kravchenko and B. V. Petrenko, Some formulas for the minimal number of generators of the direct sum of matrix rings, preprint (2007), 23 pages.[arXiv]
  21. Sefi Ladkani, On the periodicity of Coxeter transformations and the non-negativity of their Euler forms, Linear Algebra Appl. 428 (2008), no. 4, 742–753.[MR]
  22. Zhongshan Li, Frank Hall, and Fuzhen Zhang, Sign patterns of nonnegative normal matrices, in Proceedings of the Fifth Conference of the International Linear Algebra Society (Atlanta, GA, 1995), vol. 254, 1997, pp. 335–354.[MR]
  23. Frank Lübeck, On the computation of elementary divisors of integer matrices, J. Symbolic Comput. 33 (2002), no. 1, 57–65.[MR]
  24. Max Neunhöffer and Cheryl E. Praeger, Computing minimal polynomials of matrices, LMS J. Comput. Math. 11 (2008), 252–279.[MR]
  25. Michael E. O'Sullivan, Algebraic construction of sparse matrices with large girth, IEEE Trans. Inform. Theory 52 (2006), no. 2, 718–727.[MR/link]
  26. Clément Pernet and Arne Storjohann, Faster algorithms for the characteristic polynomial, ISSAC 2007, ACM, New York, 2007, pp. 307–314.[MR]
  27. Håvard Raddum and Igor Semaev, Solving multiple right hand sides linear equations, Des. Codes Cryptogr. 49 (2008), no. 1-3, 147–160.[MR/eprint]
  28. Michael Schmid, Rainer Steinwandt, Jörn Müller-Quade, Martin Rötteler, and Thomas Beth, Decomposing a matrix into circulant and diagonal factors, Linear Algebra Appl. 306 (2000), no. 1-3, 131–143.[MR]
  29. Igor Semaev, Sparse boolean equations and circuit lattices, IACR (2009), 15 pages.[eprint]
  30. Allan Steel, A new algorithm for the computation of canonical forms of matrices over fields, J. Symbolic Comput. 24 (1997), no. 3-4, 409–432.[MR]
  31. Patrick Theobald, Ein framework zur berechnung der hermite-normalform von grössen, dünnbesetzten, ganzzahligen matrizen, PhD Thesis, Technischen Universität Darmstadt, 2000.[link]
  32. Gilles Villard, Certification of the QR factor R and of lattice basis reducedness, ISSAC 2007, ACM, New York, 2007, pp. 361–368.[MR/arXiv]