Bibliography for the Power Method

short

  1. The inverse power method for calculation of multiplication factors
    Allen, E.J.; Berry, R.M.
    Annals of Nuclear Energy, v 29, n 8, May, 2002, p 929-935, Compendex.
  2. Modifying the power method in max algebra
    Elsner, L.; Van den Driessche, P.
    Linear Algebra and Its Applications, v 332-334, Aug 1, 2001, p 3-13, Compendex.  
  3. Controllability of matrix eigenvalue algorithms: the inverse power method.  
    Helmke, U.; Fuhrmann, P. A.
    Systems Control Lett.  41  (2000),  no. 1, 57--66, MathSciNet.  
  4. New look at the power method for fast subspace tracking
    Hua, Yingbo; Xiang, Yong; Chen, Tianping; Abed-Meraim, Karim; Miao, Yongfeng
    Digital Signal Processing: A Review Journal, v 9, n 4, Oct, 1999, p 297-314, Compendex.
  5. On the power method in max algebra. Special issue dedicated to Hans Schneider (Madison, WI, 1998).
    Elsner, Ludwig; van den Driessche, P.
    Linear Algebra Appl. 302/303 (1999), 17--32, MathSciNet.  
  6. Misapplication of the power method
    Ward, J. P.
    International Journal of Mathematical Education in Science and Technology, v 29, n 2, 1998, p 295, Compendex.
  7. On an integrable discretization of the Rayleigh quotient gradient system and the power method with a shift
    Nakamura, Y.; Kajiwara, K.; Shiotani, H.
    Journal of Computational and Applied Mathematics, v 96, n 2, Sep 15, 1998, p 77-90, Compendex.
  8. Estimating an eigenvector by the power method with a random start.    
    Del Corso, Gianna M.    
    SIAM J. Matrix Anal. Appl. 18 (1997), no. 4, 913--937, MathSciNet.  
  9. Monotone power method in indefinite metric and inertia theorem for matrices.
    Ben-Artzi, A.; Gohberg, I.
    Proceedings of the Fourth Conference of the International Linear Algebra Society (Rotterdam, 1994). Linear Algebra Appl. 241/243 (1996), 153--166, MathSciNet.  
  10. Some Perspectives on the Eigenvalue Problem  
    David S. Watkins  
    SIAM Review, Vol. 35, No. 3. (Sep., 1993), pp. 430-471, Jstor.  
  11. A new Monte Carlo power method for the eigenvalue problem of transfer matrices.    
    Koma, Tohru    
    J. Statist. Phys. 71 (1993), no. 1-2, 269--297, MathSciNet.  
  12. Inverse power method and weighted Sobolev spaces.
    Ding, Yi
    Acta Math. Sci. (English Ed.) 12 (1992), no. 1, 7--21, MathSciNet.  
  13. Technique to shift an eigenvalue of a complex matrix to accelerate convergence of the power and inverse power method
    Bunch, K.J.; Grow, R.W.
    Computers & Mathematics with Applications, v 21, n 4, 1991, p 11, Compendex.
  14. Easy Algorithms for Finding Eigenvalues (in Notes)  
    Clifford Reiter  
    Mathematics Magazine, Vol. 63, No. 3. (Jun., 1990), pp. 173-178, Jstor.  
  15. Rayleigh Quotient Iteration for Nonsymmetric Matrices  
    Steve Batterson; John Smillie  
    Mathematics of Computation, Vol. 55, No. 191. (Jul., 1990), pp. 169-178, Jstor.  
  16. Quotient-difference type generalizations of the power method and their analysis
    Sidi, A.; Ford, W.F.
    Journal of Computational and Applied Mathematics, v 32, n 1-2, Nov 26, 1990, p 261-272, Compendex.
  17. The Dynamics of Rayleigh Quotient Iteration  
    Steve Batterson; John Smillie  
    SIAM Journal on Numerical Analysis, Vol. 26, No. 3. (Jun., 1989), pp. 624-636, Jstor.  
  18. The acceleration of matrix power methods by cyclic variations of the shift parameter.
    Craig, I. J. D.; Sneyd, A. D.
    Comput. Math. Appl. 17 (1989), no. 7, 1149--1159, MathSciNet.  
  19. The inverse power method for semilinear elliptic equations.
    Eydeland, Alexander; Spruck, Joel
    Nonlinear diffusion equations and their equilibrium states, I (Berkeley, CA, 1986), 273--286, Math. Sci. Res. Inst. Publ., 12, Springer, New York, 1988, MathSciNet.  
  20. Criteria for Combining Inverse and Rayleigh Quotient Iteration  
    Daniel B. Szyld  
    SIAM Journal on Numerical Analysis, Vol. 25, No. 6. (Dec., 1988), pp. 1369-1375, Jstor.  
  21. The Power Method for Finding Eigenvalues on a Microcomputer (in The Teaching of Mathematics)  
    Gareth Williams, Donna Williams  
    American Mathematical Monthly, Vol. 93, No. 7. (Aug. - Sep., 1986), pp. 562-564, Jstor.  
  22. Aggregation/Disaggregation for Eigenvalue Problems  
    Francoise Chatelin; Willard L. Miranker  
    SIAM Journal on Numerical Analysis, Vol. 21, No. 3. (Jun., 1984), pp. 567-582, Jstor.  
  23. Isospectral Flows  
    David S. Watkins  
    SIAM Review, Vol. 26, No. 3. (Jul., 1984), pp. 379-391, Jstor.  
  24. A Nonlinear Inverse Power Method with Shift  
    Jean Descloux, Jacques Rappaz  
    SIAM Journal on Numerical Analysis, Vol. 20, No. 6. (Dec., 1983), pp. 1147-1152, Jstor.  
  25. The projective power method for the algebraic eigenvalue problem.
    Pan, V. Ya.
    Comput. Math. Appl. 9 (1983), no. 6, 735--745, MathSciNet.  
  26. Understanding the QR Algorithm  
    David S. Watkins  
    SIAM Review, Vol. 24, No. 4. (Oct., 1982), pp. 427-440, Jstor.  
  27. On a Finite Element Method to Solve the Criticality Eigenvalue Problem for the Transport Equation  
    Jean Descloux; Mitchell Luskin  
    SIAM Journal on Numerical Analysis, Vol. 19, No. 6. (Dec., 1982), pp. 1208-1219, Jstor.  
  28. On Estimating the Largest Eigenvalue with the Lanczos Algorithm  
    B. N. Parlett; H. Simon; L. M. Stringer  
    Mathematics of Computation, Vol. 38, No. 157. (Jan., 1982), pp. 153-165, Jstor.  
  29. General Rayleigh Quotient Iteration  
    Peter B. Geltner  
    SIAM Journal on Numerical Analysis, Vol. 18, No. 5. (Oct., 1981), pp. 839-843, Jstor.  
  30. A Class of Diagonal Transformation Methods for the Computation of the Spectral Radius of a Nonnegative Irreducible Matrix  
    Wolfgang Bunse  
    SIAM Journal on Numerical Analysis, Vol. 18, No. 4. (Aug., 1981), pp. 693-704, Jstor.  
  31. On the Rates of Convergence of the Lanczos and the Block-Lanczos Methods  
    Y. Saad  
    SIAM Journal on Numerical Analysis, Vol. 17, No. 5. (Oct., 1980), pp. 687-706, Jstor.  
  32. Estimating the Largest Eigenvalue of a Positive Definite Matrix  
    Dianne P. O'Leary; G. W. Stewart; James S. Vandergraft  
    Mathematics of Computation, Vol. 33, No. 148. (Oct., 1979), pp. 1289-1292, Jstor.  
  33. The Rayleigh Quotient Iteration and Some Generalizations for Nonnormal Matrices  
    B. N. Parlett  
    Mathematics of Computation, Vol. 28, No. 127. (Jul., 1974), pp. 679-693, Jstor.  
  34. A Geometric Theory for the QR, LU and Power Iterations  
    B. N. Parlett; W. G. Poole, Jr.  
    SIAM Journal on Numerical Analysis, Vol. 10, No. 2. (Apr., 1973), pp. 389-412, Jstor.  
  35. On Acceleration and Matrix Deflation Processes Used with the Power Method  
    Elmer E. Osborne  
    Journal of the Society for Industrial and Applied Mathematics, Vol. 6, No. 3. (Sep., 1958), pp. 279-287, Jstor.  
  36. An iterative method for the solution of linear equations based on the power method for proper vectors.
    Mendelsohn, N. S.
    Math. Tables Aids Comput. 11 (1957), 88--91, MathSciNet.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004