question about BALANC from EISPACK

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2 total messages Started by Sriram Srinivasan Thu, 07 Jan 1993 23:55

#1051

Author: Sriram Srinivasan
Date: Thu, 07 Jan 1993 23:55

18 lines
914 bytes

Hi,

   I had the following question about the BALANC routine from EISPACK.

   Given a matrix A, BALANC gives the balanced matrix

          Ab = T*A*inv(T)

   and also some information in the variables LOW, IGH, and SCALE which
   determine the similarity transformation T.

   Does anybody know how to construct a T explicity, for all A?

   Thanks.                       

   Sriram (spoiled by MATLAB)

   (ss4i@kelvin.seas.virginia.edu)

Re: question about BALANC from EISPACK

#1066

Author: G. W. Stewart
Date: Fri, 08 Jan 1993 12:15

36 lines
1540 bytes

In article <1993Jan7.235543.25287@murdoch.acc.Virginia.EDU> ss4i@kelvin.seas.Virginia.EDU (Sriram  Srinivasan) writes:
#Hi,
#
#   I had the following question about the BALANC routine from EISPACK.
#
#   Given a matrix A, BALANC gives the balanced matrix
#
#          Ab = T*A*inv(T)
#
#   and also some information in the variables LOW, IGH, and SCALE which
#   determine the similarity transformation T.
#
#   Does anybody know how to construct a T explicity, for all A?
#
#   Thanks.                       
#
#   Sriram (spoiled by MATLAB)
#
#   (ss4i@kelvin.seas.virginia.edu)

The matrix T is constructed iteratively by balancing successively
each row and its corresponding column until the process converges.
Details can be found in

   @article{pare:69,
      author = "B. N. Parlett and C. Reinsch",
      year = "1969",
      title = "Balancing a Matrix for Calculation of Eigenvalues
               and Eigenvectors",
      journal = "Numerische Mathematik",
      volume = "13",
      pages = "293--304",
      kwds = "nla, eig, scaling, software"
   }

Pete Stewart

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