Numerical methods for finding characteristic roots and vectors of matrices

Kincaid, W. M.

doi:10.1090/qam/22452

Cited by 18 publications

(15 citation statements)

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“…Wayland [3] surveys th e fi eld in its hi storical development, up to recen t years. W. U. Kincaid [4] ob Lained addiLional resuLLs by improving L h e converge nce of som e of Lh e classical procedures.…”

Section: Introductionmentioning

confidence: 99%

An iteration method for the solution of the eigenvalue problem of linear differential and integral operators

Lanczos¹

1950

J. RES. NATL. BUR. STAN.

3,910

2,238

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The p rese nt in vestigation designs a syste mat ic method for findin g the late nt I'oots and t he prin cipa l axes of a matrix, with ou t redu cin g t he o rd er of t he matri x. It is ch aracteri zed by a wide fi eld of appli ca b ili ty a nd great acc uracy, s ince t he a cc um ulat io n of ro undi ng errors is a vo id ed, t hrough t he p rocess of " minimi zed ite ratio ns". Mor eover, t he mcth od leads to a we ll co n ve rge nt s uccessiv e a pp rox im at io n p r occd ure by whi ch t he solu t io n of in tegr a l eq uatio ns of th e Fred holm t . v pe a nd t he so lu tion of t he eige n value prob lem of lin ear dilleren tia l a nd integ ra l o perators rn ay be acco m plished .

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Section: Introductionmentioning

confidence: 99%

An iteration method for the solution of the eigenvalue problem of linear differential and integral operators

Lanczos¹

1950

J. RES. NATL. BUR. STAN.

3,910

2,238

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“…To obtain the higher frequency modes, use has been made of the orthogonality relationship to (a) reduce the size of the matrix successively by one and thus obtain convergence to the higher modes, 1 ' 2 (b) "sweep" lower modes from the trial modes and thus obtain convergence to higher modes, 3 ' 4 or (c) modify the original matrix without changing its size so that the lower modes are successively removed. 5 The codes to be described in this paper are based on the matrix iteration scheme together with a variation of the matrix modification scheme given by Kincaid in reference 5. The rigid body modes are eliminated as described in Appendix III of reference 6.…”

Section: Introductionmentioning

confidence: 99%

Computation of Vibration Modes and Frequencies on SEAC

Cahill

Lévy

1955

Journal of the Aeronautical Sciences

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A description is given of several codes developed for use in the Standards Eastern Automatic Computer for computing the free vibration modes and frequencies of aircraft structures.The codes are general in nature and apply without modification to any aircraft structure whose influence coefficients, mass distribution, and geometry are specified. The codes are applicable when no more than 63 mass points are needed to define the displacement of the half-wing. In an example with seven mass points along the fuselage axis and 24 mass points for each half-wing, the computing time for the first six symmetric and the first six antisymmetric modes was 6 hours.

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“…In previous papers by Kincaid (1) and Flanders and Shortley (2) the polynomial operator was used to obtain the characteristic roots and vectors of matrices and characteristic value equations. The following development will show the application of this operator to the inhomogeneous problem.…”

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confidence: 99%