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Algorithmic solution of highertype equations
, 2011
"... In recent work we developed the notion of exhaustible set as a highertype computational counterpart of the topological notion of compact set. In this paper we give applications to the computation of solutions of highertype equations. Given a continuous functional f: X → Y and y ∈ Y, we wish to co ..."
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In recent work we developed the notion of exhaustible set as a highertype computational counterpart of the topological notion of compact set. In this paper we give applications to the computation of solutions of highertype equations. Given a continuous functional f: X → Y and y ∈ Y, we wish
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning
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
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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gradient 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
Instancebased learning algorithms
 Machine Learning
, 1991
"... Abstract. Storing and using specific instances improves the performance of several supervised learning algorithms. These include algorithms that learn decision trees, classification rules, and distributed networks. However, no investigation has analyzed algorithms that use only specific instances to ..."
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Cited by 1359 (18 self)
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Abstract. Storing and using specific instances improves the performance of several supervised learning algorithms. These include algorithms that learn decision trees, classification rules, and distributed networks. However, no investigation has analyzed algorithms that use only specific instances
The rendering equation
 Computer Graphics
, 1986
"... ABSTRACT. We present an integral equation which generallzes a variety of known rendering algorithms. In the course of discussing a monte carlo solution we also present a new form of variance reduction, called Hierarchical sampling and give a number of elaborations shows that it may be an efficient n ..."
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Cited by 908 (0 self)
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ABSTRACT. We present an integral equation which generallzes a variety of known rendering algorithms. In the course of discussing a monte carlo solution we also present a new form of variance reduction, called Hierarchical sampling and give a number of elaborations shows that it may be an efficient
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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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
Factor Graphs and the SumProduct Algorithm
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple c ..."
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Cited by 1787 (72 self)
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computational rule, the sumproduct algorithm operates in factor graphs to computeeither exactly or approximatelyvarious marginal functions by distributed messagepassing in the graph. A wide variety of algorithms developed in artificial intelligence, signal processing, and digital communications can
A learning algorithm for Boltzmann machines
 Cognitive Science
, 1985
"... The computotionol power of massively parallel networks of simple processing elements resides in the communication bandwidth provided by the hardware connections between elements. These connections con allow a significant fraction of the knowledge of the system to be applied to an instance of a probl ..."
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Cited by 586 (13 self)
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to a general learning rule for modifying the connection strengths so as to incorporate knowledge obout o task domain in on efficient way. We describe some simple examples in which the learning algorithm creates internal representations thot ore demonstrobly the most efficient way of using
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