Computing Eigenvalues of Complex Matrices by Determinant Evaluation and by Methods of Danilewski and Wielandt

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Previous article Next article Computing Eigenvalues of Complex Matrices by Determinant Evaluation and by Methods of Danilewski and WielandtWerner L. FrankWerner L. Frankhttps://doi.org/10.1137/0106026PDFPDF PLUSBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] E. Bodewig, Matrix calculus, North-Holland Publishing Company, Amsterdam, 1956xii+334 MR0080363 0086.32501 Google Scholar[2A] E. Bodewig, Bericht über die Methoden zur numerischen Lösung von algebraischen Eigenwertproblemen. I, Atti Sem. Mat. Fis. Univ. Modena, 4 (1950), 133–193 MR0048163 0041.24202 Google Scholar[2B] E. Bodewig, Bericht über die Methoden zur numerischen Lösung von algebraischen Eigenwertproblemen. II, Atti Sem. Mat. Fis. Univ. Modena, 5 (1951), 3–39 MR0055800 Google Scholar[3] R. A. Brooker and , F. H. Sumner, The method of Lanczos for calculating the characteristic roots and vectors of a real symmetric matrix, Proc. Inst. Elec. Engrs. B., 103 (1956), 114–119 MR0087217 Google Scholar[4] Robert L. Causey, Computing eigenvalues of non-Hermitian matrices by methods of Jacobi type, J. Soc. Indust. Appl. Math., 6 (1958), 172–181 10.1137/0106010 MR0103583 0097.32701 LinkISIGoogle Scholar[5] W. L. Frank, 1103A Subroutine: Algebraic Equation Solver, The Ramo-Wool-dridge Corporation, Los Angeles, California, 1958, January Google Scholar[6] Werner L. Frank, Finding zeros of arbitrary functions, J. Assoc. Comput. Mach., 5 (1958), 154–160 MR0144457 0088.33601 CrossrefISIGoogle Scholar[7] W. L. Frank, 1103A Subroutine: Complex, Floating Point Determinant Evaluator, The Ramo-Wooldridge Corporation, Los Angeles, California, 1957, December Google Scholar[8] Wallace Givens, The characteristic value-vector problem, J. Assoc. Comput. Mach., 4 (1957), 298–307 MR0092224 CrossrefISIGoogle Scholar[9] Wallace Givens, Computation of plane unitary rotations transforming a general matrix to triangular form, J. Soc. Indust. Appl. Math., 6 (1958), 26–50 10.1137/0106004 MR0092223 0087.11902 LinkISIGoogle Scholar[10] Robert T. Gregory, Results using Lanczos' method for finding eigenvalues of arbitrary matrices, J. Soc. Indust. Appl. Math., 6 (1958), 182–188 10.1137/0106011 MR0103584 0085.10805 LinkISIGoogle Scholar[11] M. Hyman, Eigenvalues and eigenvectors of general matrices, presented at the 12th National Meeting of the Association for Computing Machinery, Houston, Texas, 1957, June Google Scholar[12] Cornelius Lanczos, An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, J. Research Nat. Bur. Standards, 45 (1950), 255–282 MR0042791 CrossrefISIGoogle Scholar[13] David E. Muller, A method for solving algebraic equations using an automatic computer, Math. Tables Aids Comput., 10 (1956), 208–215 MR0083822 0072.34002 CrossrefGoogle Scholar[14] Elmer E. Osborne, On acceleration and matrix deflation processes used with the power method, J. Soc. Indust. Appl. Math., 6 (1958), 279–287 10.1137/0106019 MR0096354 0086.11001 LinkISIGoogle Scholar[15] Alexander Ostrowski, Über näherungsweise Auflösung von Systemen homogener linearer Gleichungen, Z. Angew. Math. Phys., 8 (1957), 280–285 10.1007/BF01600614 MR0090861 0081.12304 CrossrefGoogle Scholar[16] J. H. Wilkinson, Matrix programs at the National Physical Laboratory, presented at the Wayne State University Conference on Matrix Computations, 1957, Septemper 3-6 Google Scholar[17] J. H. Wilkinson, The calculation of eigenvectors by the method of Lanczos, Comput. J, 1 (1958), 148–152 10.1093/comjnl/1.3.148 MR0102915 0117.11002 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Localization Criteria and Containment for Rayleigh Quotient IterationSIAM Journal on Matrix Analysis and Applications, Vol. 10, No. 1 | 17 July 2006AbstractPDF (1766 KB)A Generalization of the Frank MatrixSIAM Journal on Scientific and Statistical Computing, Vol. 7, No. 3 | 14 July 2006AbstractPDF (479 KB)A Note on the Matrices Denoted $B_n $SIAM Journal on Applied Mathematics, Vol. 20, No. 1 | 12 July 2006AbstractPDF (378 KB)A Jacobi-Like Method for the Automatic Computation of Eigenvalues and Eigenvectors of an Arbitrary MatrixJournal of the Society for Industrial and Applied Mathematics, Vol. 10, No. 1 | 13 July 2006AbstractPDF (946 KB)The Design of a Computer Program to Determine the Natural Frequencies and Normal Modes of Vibration of an In-Line Mechanical System of Springs and MassesJournal of the Society for Industrial and Applied Mathematics, Vol. 9, No. 2 | 10 July 2006AbstractPDF (1469 KB)On Acceleration and Matrix Deflation Processes Used with the Power MethodElmer E. 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