\begin{thebibliography}{10}

\bibitem{alsen71a}
B.~M. Als\'{e}n, {\em Multiple step gradient iterative methods for computing
  eigenvalues of large symmetric matrices}, Tech. Rep. UMINF-15, University of
  Ume{\aa}, 1971.

\bibitem{andersson71}
I.~Andersson, {\em Experiments with the conjugate gradient algorithm for the
  determination of eigenvalues of symmetric matrices}, Tech. Rep. UMINF-4.71,
  University of Ume{\aa}, 1971.

\bibitem{arias92a}
T.~A. Arias, M.~C. Payne, and J.~D. Joannopoulous, {\em {\em Ab initio\/}
  molecular dynamics: analytically continued energy functionals and insights
  into iterative solutions}, Physical Review Letters, 71 (1992),
  pp.~1077--1080.

\bibitem{bradbury66a}
W.~W. Bradbury and R.~Fletcher, {\em New iterative methods for solutions of the
  eigenproblem}, Numerische Mathematik, 9 (1966), pp.~259--267.

\bibitem{chatelin84}
F.~Chatelin, {\em Simultaneous newton's iteration for the eigenproblem},
  Computing, Suppl., 5 (1984), pp.~67--74.

\bibitem{chatelin93}
\leavevmode\vrule height 2pt depth -1.6pt width 23pt, {\em Eigenvalues of
  Matrices}, John Wiley \& Sons, New York, 1993.

\bibitem{chen86}
H.~Chen, T.~K. Sarkar, S.~A. Dianat, and J.~D. Brul\'e, {\em Adaptive spectral
  estimation by the conjugate gradient method}, IEEE Trans. Acoustics, Sppech,
  and Signal Processing, ASSP-34 (1986), pp.~272--284.

\bibitem{cullum78}
J.~K. Cullum, {\em The simultaneous computation of a few of the algebraically
  largest and smallest eigenvalues of a large, sparse, symmetric matrix}, BIT,
  18 (1978), pp.~265--275.

\bibitem{cullum74b}
J.~K. Cullum and W.~E. Donath, {\em A block generalization of the symmetric
  s-step lanczos algorithm}, Tech. Rep. RC 4845, IBM Research, Yorktown
  Heights, New York, 1974.

\bibitem{cullum74a}
\leavevmode\vrule height 2pt depth -1.6pt width 23pt, {\em A block lanczos
  algorithm for computing the $q$ algebraically largest eigenvalues and a
  corresponding eigenspace of large, sparse, real symmetric matrices}, in
  Proceedings of the 1974 Conference on Decision and Control, Phoeniz, Arizona,
  November 1974, pp.~505--509.

\bibitem{cullum85}
J.~K. Cullum and R.~A. Willoughby, {\em Lanczos Algorithms for Large Symmetric
  Eigenvalue Computations}, vol.~1 Theory, Birkh{\"a}user, Stuttgart, 1985.

\bibitem{demmel87}
J.~W. Demmel, {\em Three methods for refining estimates of invariant
  subspaces}, Computing, 38 (1987), pp.~43--57.

\bibitem{dongarra83}
J.~J. Dongarra, C.~B. Moler, and J.~H. Wilkinson, {\em Improving the accuracy
  of computed eigenvalues and eigenvectors}, SIAM J. Num. Analysis, 20 (1983),
  pp.~46--58.

\bibitem{us95}
A.~Edelman, T.~A. Arias, and S.~T. Smith, {\em Conjugate gradient on the
  {S}tiefel and {G}rassmann manifolds}, {\rm submitted to} SIAM J. Matrix Anal.
  Appl.,  (1995).

\bibitem{foxkapoor69}
R.~Fox and M.~P. Kapoor, {\em A miminimization method for the solution of the
  eigenproblem arising in structural dynamics}, in Proceedings of the Second
  Conference on Matrix Methods in Structural Mechanics, L.~Berke, R.M.Bader,
  W.~J. Mykytow, J.~Przemieniecki, and M.~H. Shirk, eds., Wright-Patterson Air
  Force Base, Ohio, 1969, pp.~271--306.

\bibitem{fried69}
I.~Fried, {\em Gradient methods for finite element eigenproblems}, AIAA
  Journal, 7 (1969), pp.~739--741.

\bibitem{fried72}
\leavevmode\vrule height 2pt depth -1.6pt width 23pt, {\em Optimal gradient
  minimization scheme for finite element eigenproblems}, J. Sound Vib, 20
  (1972), pp.~333--342.

\bibitem{fu95}
Z.~Fu and E.~M. Dowling, {\em Conjugate gradient eigenstructure tracking for
  adaptive spectral estimation}, IEEE Trans.\ Signal Processing, 43 (1995),
  pp.~1151--1160.

\bibitem{fuhrmann84}
D.~R. Fuhrmann and B.~Liu, {\em An iterative algorithm for locating the minimal
  eigenvector of a symmetric matrix}, in Proc. IEEE Int. Conf. Acoust., Speech,
  Signal Processing, 1984, pp.~45.8.1--4.

\bibitem{geradin71a}
M.~Geradin, {\em The computational efficiency of a new minimization algorithm
  for eigenvalue analysis}, J. Sound Vibration, 19 (1971), pp.~319--331.

\bibitem{gillan89a}
M.~J. Gillan, {\em Calculation of the vacancy formation energy in aluminium},
  Journal of Physics, Condensed Matter, 1 (1989), pp.~689--711.

\bibitem{golub89}
G.~Golub and D.~O'Leary, {\em Some history of the conjugate gradient and
  lanczos methods}, SIAM Review, 31 (1989), pp.~50--102.

\bibitem{cohen87}
R.~Haimi-Cohen and A.~Cohen, {\em Gradient-type algorithms for partial singular
  value decomposition}, IEEE Trans. Pattern. Anal. Machine Intell., PAMI-9
  (1987), pp.~137--142.

\bibitem{karush51}
W.~Karush, {\em An iterative method for finding characteristic vectors of a
  symmetric matrix}, Pacific J. Math., 1 (1951), pp.~233--248.

\bibitem{kresse93}
G.~Kresse and J.~Hafner, {\em Ab initio molecular dynamics for liquid metals},
  Physical Review B,  (1993), pp.~558--561.

\bibitem{sung94}
M.W.Sung, R.~Kawai, and J.~Weare, {\em Packing transitions in nanosized li
  clusters}, Physical Review Letter, 73 (1994), pp.~3552--3555.

\bibitem{nocedal91}
J.~Nocedal, {\em Theory of algorithms for unconstrained optimization}, Acta
  Numerica,  (1992), pp.~199--242.

\bibitem{parlett80}
B.~N. Parlett, {\em The Symmetric Eigenvalue Problem}, Prentice-Hall, Inc.,
  Englewood Cliffs, NJ, 1980.

\bibitem{ptaaj}
M.~C. Payne, M.~P. Teter, D.~C. Allan, T.~A. Arias, and J.~D. Joannopoulos,
  {\em Iterative minimization techniques for {\it ab initio} total-energy
  calculations: molecular dynamics and conjugate gradients}, Rev. Mod. Phys, 64
  (1992), pp.~1045--1097.

\bibitem{perdon86}
A.~Perdon and G.~Gambolati, {\em Extreme eigenvalues of large sparse matrices
  by rayleigh quotient and modified conjugate gradients}, Comp. Methods Appl.
  Mech. Engin., 56 (1986), pp.~251--264.

\bibitem{ruhe74}
A.~Ruhe, {\em Iterative eigenvalue algorithms for large symmetric matrices}, in
  Numerische Behandlung von Eigenwertaaufgaben Oberwolfach 1972, Intl, Series
  Numerical Math. Volume 24, 1974, pp.~97--115.

\bibitem{sameh82a}
A.~H. Sameh and J.~A. Wisniewski, {\em A trace minimization algorithm for the
  generalized eigenvalue problem}, SIAM Journal of Numerical Analysis, 19
  (1982), pp.~1243--1259.

\bibitem{smith93a}
S.~T. Smith, {\em Geometric Optimization Methods for Adaptive Filtering}, PhD
  thesis, Harvard University, Cambridge, Massachusetts, 1993.

\bibitem{smith94a}
\leavevmode\vrule height 2pt depth -1.6pt width 23pt, {\em Optimization
  techniques on {R}iemannian manifolds}, in Hamiltonian and Gradient Flows,
  Algorithms and Control, A.~Bloch, ed., vol.~3 of Fields Institute
  Communications, Providence, RI, 1994, American Mathematical Society,
  pp.~113--146.

\bibitem{stewart73}
G.~W. Stewart, {\em Error and perturbation bounds for subspaces associated with
  certain eigenvalue problems}, SIAM Review, 15 (1973), pp.~752--764.

\bibitem{stich89a}
I.~{\v{S}tich}, R.~Car, M.~Parrinello, and S.~Baroni, {\em Conjugate gradient
  minimization of the energy functional: A new method for electronic structure
  calculation}, Phys. Rev. B., 39 (1989), pp.~4997--5004.

\bibitem{teter89a}
M.~P. Teter, M.~C. Payne, and D.~C. Allan, {\em {Solution of
  {S}chr\"{o}dinger's equation for large systems}}, Phys. Review B, 40 (1989),
  pp.~12255--12263.

\bibitem{townsend78}
M.~Townsend and G.~E. Johnson, {\em In favor of conjugate directions: A
  generalized acceptable-point algorithm for function minimization}, J.
  Franklin Inst., 306 (1978).

\bibitem{yang89}
X.~Yang, T.~P. Sarkar, and E.~Arvas, {\em A survey of conjugate gradient
  algorithms for solution of extreme eigen-problems of a symmetric matrix},
  IEEE Trans. Acoust., Speech, Signal Processing, 37 (1989), pp.~1550--1556.

\end{thebibliography}
