Lambda-matrices and vibrating systems

By Peter Lancaster. 2002

405 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/50ffde03722153bd6b18ea41b7d8b792fdf24569

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In Control and Systems Engineering

In Mechanics of Materials

Citations in the corpus

POLYNOMIAL EIGENVALUE PROBLEMS WITH HAMILTONIAN STRUCTURE (2002, result): “This linearization is essentially the same as that given in Theorem 4.2 of [ 8 ].”
Nonlinear eigenvalue problems: a challenge for modern eigenvalue methods (2004, background): “which is the Rayleigh functional for general nonlinear eigenproblems proposed in [48], and which can be interpreted as one Newton step for solving the equation fk(λ) := y H k F(λ)xk = 0.”
Inverse problems for damped vibrating systems (2005, neutral): “[6] for an early account.”
Spectral equivalence of matrix polynomials and the index sum theorem (2014, background): “Many matrix polynomials arising in applications have some kind of extra structure, a fact that was noticed in very early work on matrix polynomials [28].”
Backward error and condition of polynomial eigenvalue problems (2000, methodology): “In many applications [16,18,23], the matrices A;B and C are Hermitian.”
Eigenvalue computation in the 20th century (2000, methodology): “We mention the work of Lancaster [77], Kublanovskaja [75,76], and Ruhe [107].”
Detecting a definite Hermitian pair and a hyperbolic or elliptic quadratic eigenvalue problem, and associated nearness problems (2002, background): “Forn > 2 the answer is yes, and indeed hyperbolicity is sometimes defined in terms of real x whenQ is real (see [7,8,14], for example).”
Spectra and Pseudospectra (2020, background): “Taussky (at Caltech) and Lancaster (at the University of Calgary) both went on to make fundamental contributions to matrix theory and in particular to matrix eigenvalue problems [24], [17].”
The Quadratic Eigenvalue Problem (2001, methodology): “Following Lancaster [88], we introduce two classes of Hermitian QEPs corresponding to the cases Λ(Q) ⊂ R and Λ(Q) ∩ R = ∅.”
Bounds for eigenvalues of matrix polynomials (2003, background): “from scalars to matrices we obtain the polynomial eigenvalue problem, which has also received much attention—see, for example, the books [6,13].”
A spectrally formulated plate element for wave propagation analysis in anisotropic material (2005, methodology): “In the first method, it is noted that the desired eigenvalues are the latent roots, which satisfy the condition det(W(k)) = 0, (see [ 34 ]).”
Numerical analysis of a quadratic matrix equation (2000, background): “A second application is the solution of the quadratic eigenvalue problem (2), which arises in the analysis of damped structural systems and vibration problems (Datta, 1995, Chapter 9; Lancaster, 1966).”
Vector Spaces of Linearizations for Matrix Polynomials (2006, positive): “We show how to simply construct two vector spaces of pencils that generalize the companion forms of P , and prove that almost all of these pencils are linearizations for P .”