A modified method for reconstructing periodic Jacobi matrices
Authors:
Daniel Boley and Gene H. Golub
Journal:
Math. Comp. 42 (1984), 143150
MSC:
Primary 65F15; Secondary 15A18
MathSciNet review:
725989
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Abstract: In this note, we discuss the reconstruction of periodic Jacobi matrices from spectral data. The method combines ideas and techniques from the algorithms given by Boley and Golub [1], [2], and Ferguson [3], resulting in a numerically stable algorithm applicable to a larger class of problems. The number of initial data items needed for this method equals the number of items in the resulting matrix, namely 2n.
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D. Boley & G. H. Golub, The Matrix Inverse Eigenvalue Problem for Periodic Matrices, invited paper at Fourth Conference on Basic Problems of Numerical Anaysis (LIBLICE IV), Pilsin, Czechoslovakia, Sept. 1978.
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 [1]
 D. Boley & G. H. Golub, Inverse Eigenvalue Problems for Band Matrices, Lecture Notes in Mathematics, Numerical Analysis (Dundee, 1977), SpringerVerlag, Berlin and New York, 1977. MR 0474741 (57:14375)
 [2]
 D. Boley & G. H. Golub, The Matrix Inverse Eigenvalue Problem for Periodic Matrices, invited paper at Fourth Conference on Basic Problems of Numerical Anaysis (LIBLICE IV), Pilsin, Czechoslovakia, Sept. 1978.
 [3]
 W. Ferguson Jr., "The construction of Jacobi and periodic Jacobi matrices with prescribed spectra," Math Comp., v. 35, 1980, pp. 12031220. MR 583498 (82c:65027)
 [4]
 F. W. BieglerKönig, "Construction of band matrices from spectral data," Linear Algebra Appl., v. 40, 1981, pp. 7984. MR 629608 (83a:65033)
 [5]
 John Thompson, personal communication.
 [6]
 G. W. Stewart, Introduction to Matrix Computations, Academic Press, New York, 1973. MR 0458818 (56:17018)
 [7]
 C. Lanczos, "An iteration method for the solution of the eigenvalue problem of linear differential and integral operators," J. Res. Nat. Bur. Standards, v. 45, 1950, pp. 255282. MR 0042791 (13:163d)
 [8]
 J. H. Wilkinson, The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, 1965. MR 0184422 (32:1894)
 [9]
 H. Flaschka, "The Toda lattice," Phys. Rev. B, v. 9, 1974, pp. 19241925. MR 0408647 (53:12411)
 [10]
 H. Flaschka & D. W. McLaughlin, "Canonically conjugate variables for the Kortwegde Vries equation and the Toda lattice with periodic boundary conditions," Progr. Theoret. Phys., v. 55, 1976, pp. 438456. MR 0403368 (53:7179)
 [11]
 H. Simon, The Lanczos Algorithm for Solving Symmetric Linear Systems, Ph.D Thesis, Center for Pure and Applied Mathematics, Univ. of Calif., Berkeley report no. PAM74, April 1982.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198407259891
PII:
S 00255718(1984)07259891
Article copyright:
© Copyright 1984
American Mathematical Society
