REFERENCES

NOTE: This list is new will hopefully grow rapidly. I would like to move towards
      making Elemental (and my other open source efforts) closer to 
      publications.

[1] Paolo Bientinesi, Brian Gunter, and Robert A. van de Geijn, 
    "Families of algorithms related to the inversion of a Symmetric Positive
     Definite matrix", ACM Transactions on Mathematical Software, Vol. 35, 
    Issue 1, pp. 3:1--3:22, 2008.

    NOTE: The variant 2 algorithm from Fig. 9 was parallelized for Elemental's
          HPD inversion.

[2] Tony F. Chan, "An improved algorithm for computing the Singular Value
    Decomposition", ACM Transactions on Mathematical Software, Vol. 8, Issue 1, 
    pp. 72--83, 1982.
    http://www.stat.uchicago.edu/~lekheng/courses/324/chan.pdf

    NOTE: This paper introduced the idea of using a QR decomposition as a first
          step in the SVD of a non-square matrix in order to accelerate the 
          computation.

[3] Gene H. Golub and Christian Reinsch, "Singular value decomposition and 
    least squares solutions", Numerische Mathematik, Vol. 14, No. 5, 
    pp. 403--420, 1970.

    NOTE: This paper introduced the standard algorithm for computing the SVD.

[4] Gene H. Golub and Charles F. van Loan, "Matrix Computations", 3rd edition,
    Johns Hopkins University Press, Baltimore, 1996.

    NOTE: Added for definition of Kahan matrix (pg. 260)

[5] Ming Gu and Stanley Eisenstat, "Efficient algorithms for computing a strong
    rank-revealing QR factorization", SIAM Journal on Scientific Computing, 
    Vol. 17, Issue 4, pp. 848--869, 1996.

    NOTE: Standard reference for RRQR factorizations, which will hopefully be
          added to Elemental in the near future.

[6] Zhongxiao Jia, "Using cross-product matrices to compute the SVD",
    Numerical Algorithms, 42:31--61, 2006.
    http://faculty.math.tsinghua.edu.cn/~zjia/jianumalgo.pdf

    NOTE: This paper could serve as a foundation for achieving high absolute
          accuracy in a cross-product based algorithm for computing the SVD.
          Such an approach should be more scalable than the current 
          bidiagonalization-based approach.