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An iterative method for the solution of the eigenvalue problem of linear differential and integral
, 1950
"... The present investigation designs a systematic method for finding the latent roots and the principal axes of a matrix, without reducing the order of the matrix. It is characterized by a wide field of applicability and great accuracy, since the accumulation of rounding errors is avoided, through the ..."
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Cited by 537 (0 self)
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the process of "minimized iterations". Moreover, the method leads to a well convergent successive approximation procedure by which the solution of integral equations of the Fredholm type and the solution of the eigenvalue problem of linear differential and integral operators may be accomplished. I.
Compressive sensing
 IEEE Signal Processing Mag
, 2007
"... The Shannon/Nyquist sampling theorem tells us that in order to not lose information when uniformly sampling a signal we must sample at least two times faster than its bandwidth. In many applications, including digital image and video cameras, the Nyquist rate can be so high that we end up with too m ..."
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Cited by 696 (62 self)
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will learn about a new technique that tackles these issues using compressive sensing [1, 2]. We will replace the conventional sampling and reconstruction operations with a more general linear measurement scheme coupled with an optimization in order to acquire certain kinds of signals at a rate significantly
Alternatingtime Temporal Logic
 Journal of the ACM
, 1997
"... Temporal logic comes in two varieties: lineartime temporal logic assumes implicit universal quantification over all paths that are generated by system moves; branchingtime temporal logic allows explicit existential and universal quantification over all paths. We introduce a third, more general var ..."
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Cited by 620 (53 self)
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Temporal logic comes in two varieties: lineartime temporal logic assumes implicit universal quantification over all paths that are generated by system moves; branchingtime temporal logic allows explicit existential and universal quantification over all paths. We introduce a third, more general
Differentialdifference equations
, 1963
"... are solved, where either f(x) or g(x) is specified in certain intervals in the range 0 ^ x < oo, with up to four intervals. r(f) may be different for different intervals. It is shown that the solution is closely allied to that of a type of FourierBessel series with mixed boundary values so that ..."
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Cited by 331 (0 self)
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are solved, where either f(x) or g(x) is specified in certain intervals in the range 0 ^ x < oo, with up to four intervals. r(f) may be different for different intervals. It is shown that the solution is closely allied to that of a type of FourierBessel series with mixed boundary values so
Operations for Learning with Graphical Models
 Journal of Artificial Intelligence Research
, 1994
"... This paper is a multidisciplinary review of empirical, statistical learning from a graphical model perspective. Wellknown examples of graphical models include Bayesian networks, directed graphs representing a Markov chain, and undirected networks representing a Markov field. These graphical models ..."
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Cited by 276 (13 self)
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are extended to model data analysis and empirical learning using the notation of plates. Graphical operations for simplifying and manipulating a problem are provided including decomposition, differentiation, and the manipulation of probability models from the exponential family. Two standard algorithm schemas
Symplectic reflection algebras, CalogeroMoser space, and deformed HarishChandra homomorphism
 Invent. Math
"... To any finite group Γ ⊂ Sp(V) of automorphisms of a symplectic vector space V we associate a new multiparameter deformation, Hκ, of the algebra C[V]#Γ, smash product of Γ with the polynomial algebra on V. The parameter κ runs over points of CP r, where r = number of conjugacy classes of symplectic ..."
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Cited by 280 (39 self)
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‘rational ’ degenerations of the double affine Hecke algebra introduced earlier by Cherednik. Let Γ = Sn, the Weyl group of g = gl n. We construct a 1parameter deformation of the HarishChandra homomorphism from D(g) g, the algebra of invariant polynomial differential operators on the Lie algebra g = gl n
On supporting containment queries in relational database management systems
, 2001
"... Virtually all proposals for querying XML include a class of query we term “containment queries”. It is also clear that in the foreseeable future, a substantial amount of XML data will be stored in relational database systems. This raises the question of how to support these containment queries. The ..."
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Cited by 278 (6 self)
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of work on RDBMS query optimization, query execution, scalability, and concurrency control and recovery immediately extend to the queries and structures that implement these new operations. But all this will be irrelevant if the performance of option (b) lags that of (a) by too much. In this paper, we
Pseudospectra of linear operators
 SIAM Rev
, 1997
"... Abstract. If a matrix or linear operator A is far from normal, its eigenvalues or, more generally, its spectrum may have little to do with its behavior as measured by quantities such as ‖An ‖ or ‖exp(tA)‖. More may be learned by examining the sets in the complex plane known as the pseudospectra of A ..."
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Cited by 153 (10 self)
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Abstract. If a matrix or linear operator A is far from normal, its eigenvalues or, more generally, its spectrum may have little to do with its behavior as measured by quantities such as ‖An ‖ or ‖exp(tA)‖. More may be learned by examining the sets in the complex plane known as the pseudospectra
On polynomial solutions of differential equations
, 1991
"... A general method of obtaining linear differential equations having polynomial solutions is proposed. The method is based on an equivalence of the spectral problem for an element of the universal enveloping algebra of some Lie algebra in the ”projectivized” representation possessing an invariant subs ..."
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subspace and the spectral problem for a certain linear differential operator with variable coefficients. It is shown in general that polynomial solutions of partial differential equations occur; in the case of Lie superalgebras there are polynomial solutions of some matrix differential equations, quantum
On Krylov subspace approximations to the matrix exponential operator
 SIAM J. NUMER. ANAL
, 1997
"... Krylov subspace methods for approximating the action of matrix exponentials are analyzed in this paper. We derive error bounds via a functional calculus of Arnoldi and Lanczos methods that reduces the study of Krylov subspace approximations of functions of matrices to that of linear systems of equ ..."
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Cited by 183 (6 self)
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onwards, depending on the geometry of the numerical range, the spectrum or the pseudospectrum. The convergence to exp(A)v is faster than that of corresponding Krylov methods for the solution of linear equations (IA)x = v, which usually arise in the numerical solution of stiff ordinary differential
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