New matrix transformations for obtaining characteristic vectors
Authors:
William Feller and George E. Forsythe
Journal:
Quart. Appl. Math. 8 (1951), 325-331
MSC:
Primary 65.0X
DOI:
https://doi.org/10.1090/qam/39373
MathSciNet review:
39373
Full-text PDF Free Access
References |
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Additional Information
Aitken, A. C., Studies in practical mathematics II. The evaluation of the latent roots and latent vectors of a matrix, Proc. Roy. Soc. Edinburgh 57, 269-304 (1937).
Bôcher, M., Introduction to Higher Algebra, New York, 1907, Chapter XX.
Duncan, W. J. and Collar, A. R., A method for the solution of oscillation problems by matrices, Phil. Mag. [7], 17, 865-909 (1934).
Frazer, R. A., Duncan, W. J., and Collar, A. R., Elementary Matrices, Cambridge, England, 1938.
- Magnus R. Hestenes and William Karush, A method of gradients for the calculation of the characteristic roots and vectors of a real symmetric matrix, J. Research Nat. Bur. Standards 47 (1951), 45–61. MR 0043552
Hotelling, Harold, Analysis of a complex of statistical variables into principal components, J. Educational Psychology 24, 417-441, 498-520 (1933).
Hotelling, Harold, Simplified calculation of principal components, Psychometrika 1, 27-35. (1936).
- W. M. Kincaid, Numerical methods for finding characteristic roots and vectors of matrices, Quart. Appl. Math. 5 (1947), 320–345. MR 22452, DOI https://doi.org/10.1090/S0033-569X-1947-22452-3
- 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. MR 0042791
- J. Morris, Frequency equations, Aircraft Engrg. 14 (1942), 108–110. MR 7120
Morris, Joseph, The Escalator Method, New York, 1947, Chap. 10. especially pp. 115-118.
Morris, J. and Head, J. W., Lagrangian frequency equations, Aircraft Engineering 14, 312-316 (1942). An appendix by G. Temple summarizes the escalator method in matrix notation.
- K. A. Semendiaev, The determination of latent roots and invariant manifolds of matrices by means of iterations, Appl. Math. Mech. [Akad. Nauk SSSR. Prikl. Mat. Mech.] 7 (1943), 193–222 (Russian, with English summary). MR 0010662
- Ledyard R. Tucker, The determination of successive principal components without computation of tables of residual correlation coefficients, Psychometrika 9 (1944), 149–153. MR 10663, DOI https://doi.org/10.1007/BF02288719
von Mises, R., and Pollaczek-Geiringer, H., Praktische Verfahren der Gleichungsaufloesung, ZS. angew. Math. Mech. 9, 152-164 (1929).
- Helmut Wielandt, Das Iterationsverfahren bei nicht selbstadjungierten linearen Eigenwertaufgaben, Math. Z. 50 (1944), 93–143 (German). MR 17460, DOI https://doi.org/10.1007/BF01312438
Aitken, A. C., Studies in practical mathematics II. The evaluation of the latent roots and latent vectors of a matrix, Proc. Roy. Soc. Edinburgh 57, 269-304 (1937).
Bôcher, M., Introduction to Higher Algebra, New York, 1907, Chapter XX.
Duncan, W. J. and Collar, A. R., A method for the solution of oscillation problems by matrices, Phil. Mag. [7], 17, 865-909 (1934).
Frazer, R. A., Duncan, W. J., and Collar, A. R., Elementary Matrices, Cambridge, England, 1938.
Hestenes, M. R. and Karush, W., A method of gradients for the calculation of the characteristic roots and vectors of a real symmetric matrix, multilithed typescript at the National Bureau of Standards, Los Angeles, 1950.
Hotelling, Harold, Analysis of a complex of statistical variables into principal components, J. Educational Psychology 24, 417-441, 498-520 (1933).
Hotelling, Harold, Simplified calculation of principal components, Psychometrika 1, 27-35. (1936).
Kincaid, W. M., Numerical methods for finding characteristic roots and vectors of matrices, Q. Appl. Math. 5, 320-345 (1947).
Lanczos, Cornelius, An iteration method for the solution of the eigen-value problem of linear differential and integral operators, multilithed typescript at the National Bureau of Standards, Los Angeles, 1949.
Morris, J., Frequency equations, Aircraft Engineering 14, 108-110 (1942).
Morris, Joseph, The Escalator Method, New York, 1947, Chap. 10. especially pp. 115-118.
Morris, J. and Head, J. W., Lagrangian frequency equations, Aircraft Engineering 14, 312-316 (1942). An appendix by G. Temple summarizes the escalator method in matrix notation.
Semendiaev, K. A., The determination of latent roots and invariant manifolds of matrices by means of iterations, Prikladnaya matematika i mehanika (Leningrad) 7, 193-222 (1943). Russian, with brief English summary.
Tucker, Ledyard R., Determination of the successive principal components without computation of tables of residual correlation coefficients, Psychometrika 9, 149-153 (1944).
von Mises, R., and Pollaczek-Geiringer, H., Praktische Verfahren der Gleichungsaufloesung, ZS. angew. Math. Mech. 9, 152-164 (1929).
Wielandt, Helmut, Das Iterationsverfahren bei nichtselbstadjungierten linearen Eigenwertaufgaben, Math. ZS. 50, 93-143 (1944), p. 96.
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Article copyright:
© Copyright 1951
American Mathematical Society
