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Laguerre’s method applied to the matrix eigenvalue problem


Author: Beresford Parlett
Journal: Math. Comp. 18 (1964), 464-485
MSC: Primary 65.40
DOI: https://doi.org/10.1090/S0025-5718-1964-0165668-2
MathSciNet review: 0165668
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  • Report on the algorithmic language ALGOL 60, Numer. Math. 2, 106–136. Also published as Acta Polytech. Scandinav. 284 (1960), 40 pp. MR 0130074, DOI https://doi.org/10.1007/BF01386216
  • E. Durand, Solutions numériques des équations algébriques. Tome I: Équations du type $F(x)=0$; racines d’un polynôme, Masson et Cle, Editeurs, Paris, 1960 (French). MR 0121987
  • P. J. Eberlein, A Jacobi-like method for the automatic computation of eigenvalues and eigenvectors of an arbitrary matrix, J. Soc. Indust. Appl. Math. 10 (1962), 74–88. MR 139264
  • Werner L. Frank, Computing eigenvalues of complex matrices by determinant evaluation and by methods of Danilewski and Wielandt, J. Soc. Indust. Appl. Math. 6 (1958), 378–392. MR 103586
  • E. N. Laguerre, Oeuvres de Laguerre, Gauthier-Villars, Paris, Vol. 1, p. 87-103.
  • Hans J. Maehly, Zur iterativen Auflösung algebraischer Gleichungen, Z. Angew. Math. Phys. 5 (1954), 260–263 (German). MR 63146, DOI https://doi.org/10.1007/bf01600333
  • B. N. Parlett, Applications of Laguerre’s Method to the Matrix Eigenvalue Problem, Tech. Report No. 21, Stanford Univ., Applied Math. and Stat. Labs., Contract Nonr 225(37), 1962.
  • J. B. Rosser, C. Lanczos, M. R. Hestenes, and W. Karush, Separation of close eigenvalues of a real symmetric matrix, J. Research Nat. Bur. Standards 47 (1951), 291–297. MR 0048914
  • Paul A. White, The computation of eigenvalues and eigenvectors of a matrix, J. Soc. Indust. Appl. Math. 6 (1958), 393–437. MR 100350
  • J. H. Wilkinson, Determination of Characteristic Values and Characteristic Vectors, Application of Advanced Numer. Anal. to Digital Computers, Summer Session, 1958, Univ. of Michigan, Ann Arbor, Mich., p. 101-154. J. H. Wilkinson, Notes on Practical Methods of Solving Linear Systems and Calculating the Eigensystems of Matrices, National Physical Laboratory, Teddington, England, 1959. J. H. Wilkinson, Advanced Numerical Analysis, Summer Session, 1960, Univ. of Michigan, Ann Arbor, Mich.
  • J. H. Wilkinson, Error analysis of floating-point computation, Numer. Math. 2 (1960), 319–340. MR 116477, DOI https://doi.org/10.1007/BF01386233
  • J. H. Wilkinson, Stability of the reduction of a matrix to almost triangular and triangular forms by elementary similarity transformations, J. Assoc. Comput. Mach. 6 (1959), 336–359. MR 106542, DOI https://doi.org/10.1145/320986.320988
  • J. H. Wilkinson, The Numerical Eigenvalue Problem, Oxford Univ. Press, in preparation.

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Article copyright: © Copyright 1964 American Mathematical Society