The algebraic eigenvalue problem

By J. H. Wilkinson. 1966

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Citations in the corpus

Network ecology: topological constraints on ecosystem dynamics (2004, unknown): “Using the Gershgor theorems[169] Haydon has shown that if the aii 0 self-regulating coefficients are different in the m trix A then the stable webs become more stable if the interaction strength or/and connectance in Stable webs will be less stable if there are more species in the web as in May’s mo”
Analysis and Numerical Solution of Generalized Lyapunov Equations (2002, methodology): “, (A )k−1CT ] via the block Arnoldi or Lanczos process [64, 80, 171] together with solving reduced order linear matrix equations.”
A Class of Parallel Tiled Linear Algebra Algorithms for Multicore Architectures (2007, background): “When b = n (a 1{by{1 tiled matrix with n{by{n tiles), GETWP reduces to GEPP. GEWP dates back to Wilkinson’s work [ 39 ].”
Iterative Krylov Methods for Large Linear Systems (2003, background): “For general background on linear algebra for numerical applications see [98, 181], and for the effects of finite precision, for general linear systems, I refer to [116] (as a modern successor of Wilkinson’s book [222]).”
Single View Metrology (2000, methodology): “We now use matrix perturbation theory (Golub and Van Loan, 1989; Stewart and Sun, 1990; Wilkinson, 1965) to compute the covariance Λs of the solution vector s based on this zero approximation.”
On the invalidity of fuzzifying numerical judgments in the Analytic Hierarchy Process (2007, methodology): “To a first order approximation, perturbation Δw1 in the principal right eigenvector w1 due to a perturbation ΔA in the matrix A where A is consistent is given by Wilkinson [9]:”
DERIVING THE AHP 1-9 SCALE FROM FIRST PRINCIPLES (2001, background): “Wilkinson [5], involves all the eigenvalues 8j of A and all of both its left (vj) and right (wj) eigenvectors.”
Low-Rank Solution of Lyapunov Equations (2004, methodology): “The columns of UJ , as well as the quantities BJ := (UJ) B and AJ×J := U J AUJ , are obtained via the block Arnoldi process [7, 42].”
Circulant preconditioners for Hermitian Toeplitz systems (2011, background): “Wilkinson, J., The Algebraic Eigenvalue Problem, Clarendon Press, Ox-ford, 1965.”
The Second Eigenvalue of the Google Matrix (2003, methodology): “The rate of convergence of the power method is given by [13, 2].”
Matrices: Theory and Applications (2002, background): “For instance, it is not as detailed as [19] concerning numerics, or as [35] on eigenvalue problems, or as [21] about Weyl-type inequalities.”
Isogeometric shell analysis: The Reissner-Mindlin shell (2010, methodology): “Power iteration [42] obtains the maximum eigenvalue of the system by the iterative scheme ( ω(2)maxΨ )i+1 = M−1KΨi (42) (ω(2)max) i+1 = max n=1,NEQN ( (ω(2)maxΨ) i+1 n Ψn ) (43)”
Relatively robust representations of symmetric tridiagonals (2000, background): “An illustration: The matrixW+21 was introduced by Wilkinson [16] in the 1960s: diag= (10,9,8, . . . ,1,0,1, . . . ,8,9,10), the next to diagonal entries are all 1.”