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685,363
For Most Large Underdetermined Systems of Linear Equations the Minimal ℓ1norm Solution is also the Sparsest Solution
 Comm. Pure Appl. Math
, 2004
"... We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that ..."
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Cited by 560 (10 self)
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We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so
Algorithms for Quantum Computation: Discrete Logarithms and Factoring
, 1994
"... A computer is generally considered to be a universal computational device; i.e., it is believed able to simulate any physical computational device with a increase in computation time of at most a polynomial factor. It is not clear whether this is still true when quantum mechanics is taken into consi ..."
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Cited by 1103 (7 self)
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into consideration. Several researchers, starting with David Deutsch, have developed models for quantum mechanical computers and have investigated their computational properties. This paper gives Las Vegas algorithms for finding discrete logarithms and factoring integers on a quantum computer that take a number
Equationbased congestion control for unicast applications
 SIGCOMM '00
, 2000
"... This paper proposes a mechanism for equationbased congestion control for unicast traffic. Most besteffort traffic in the current Internet is wellserved by the dominant transport protocol, TCP. However, traffic such as besteffort unicast streaming multimedia could find use for a TCPfriendly cong ..."
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Cited by 832 (29 self)
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This paper proposes a mechanism for equationbased congestion control for unicast traffic. Most besteffort traffic in the current Internet is wellserved by the dominant transport protocol, TCP. However, traffic such as besteffort unicast streaming multimedia could find use for a TCP
Exact Sampling with Coupled Markov Chains and Applications to Statistical Mechanics
, 1996
"... For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has ..."
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Cited by 548 (13 self)
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, and that outputs samples in exact accordance with the desired distribution. The method uses couplings, which have also played a role in other sampling schemes; however, rather than running the coupled chains from the present into the future, one runs from a distant point in the past up until the present, where
Numerical Solutions of the Euler Equations by Finite Volume Methods Using RungeKutta TimeStepping Schemes
, 1981
"... A new combination of a finite volume discretization in conjunction with carefully designed dissipative terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an effective method for solving the Euler equations in arbitrary geometric domains. The method has been used to deter ..."
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Cited by 456 (78 self)
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A new combination of a finite volume discretization in conjunction with carefully designed dissipative terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an effective method for solving the Euler equations in arbitrary geometric domains. The method has been used
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
 ACM Trans. Math. Software
, 1982
"... An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable numerica ..."
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Cited by 649 (21 self)
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An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable numerical properties. Reliable stopping criteria are derived, along with estimates of standard errors for x and the condition number of A. These are used in the FORTRAN implementation of the method, subroutine LSQR. Numerical tests are described comparing I~QR with several other conjugategradient algorithms, indicating that I~QR is the most reliable algorithm when A is illconditioned. Categories and Subject Descriptors: G.1.2 [Numerical Analysis]: ApprorJmationleast squares approximation; G.1.3 [Numerical Analysis]: Numerical Linear Algebralinear systems (direct and
Fronts propagating with curvature dependent speed: algorithms based on Hamilton–Jacobi formulations
 Journal of Computational Physics
, 1988
"... We devise new numerical algorithms, called PSC algorithms, for following fronts propagating with curvaturedependent speed. The speed may be an arbitrary function of curvature, and the front can also be passively advected by an underlying flow. These algorithms approximate the equations of motion, w ..."
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Cited by 1183 (64 self)
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We devise new numerical algorithms, called PSC algorithms, for following fronts propagating with curvaturedependent speed. The speed may be an arbitrary function of curvature, and the front can also be passively advected by an underlying flow. These algorithms approximate the equations of motion
A comparative analysis of selection schemes used in genetic algorithms
 Foundations of Genetic Algorithms
, 1991
"... This paper considers a number of selection schemes commonly used in modern genetic algorithms. Specifically, proportionate reproduction, ranking selection, tournament selection, and Genitor (or «steady state") selection are compared on the basis of solutions to deterministic difference or d ..."
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Cited by 512 (32 self)
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or differential equations, which are verified through computer simulations. The analysis provides convenient approximate or exact solutions as well as useful convergence time and growth ratio estimates. The paper recommends practical application of the analyses and suggests a number of paths for more detailed
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5350 (67 self)
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was the exploration of variations around a point, within the bounds imposed by the constraints, in order to help characterize solutions and portray them in terms of ‘variational principles’. Notions of perturbation, approximation and even generalized differentiability were extensively investigated. Variational theory
Results 1  10
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685,363