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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 654 (21 self)
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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 conjugate
Numerical Properties of the LLL Algorithm
, 2007
"... The LLL algorithm is widely used to solve the integer least squares problems that arise in many engineering applications. As most practitioners did not understand how the LLL algorithm works, they avoided the issue by referring to the method as an integer Gram Schmidt approach (without explaining wh ..."
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Cited by 2 (1 self)
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what they mean by this term). Luk and Tracy 1 were first to describe the behavior of the LLL algorithm, and they presented a new numerical implementation that should be more robust than the original LLL scheme. In this paper, we compare the numerical properties of the two different LLL implementations.
PDDL2.1: An Extension to PDDL for Expressing Temporal Planning Domains
, 2003
"... In recent years research in the planning community has moved increasingly towards application of planners to realistic problems involving both time and many types of resources. For example, interest in planning demonstrated by the space research community has inspired work in observation scheduling, ..."
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Cited by 609 (41 self)
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the development of a modelling language capable of expressing temporal and numeric properties of planning domains. In this paper we describe the language, PDDL2.1, that was used in the competition. We describe the syntax of the language, its formal semantics and the validation of concurrent plans. We observe
Numerical properties of isotrivial fibrations
"... Abstract. A smooth, projective surface S is called a standard isotrivial fibration if there exists a finite group G which acts faithfully on two smooth projective curves C1 and C2, so that S is isomorphic to the minimal desingularization of T: = (C1 × C2)/G, where G acts diagonally on the product. W ..."
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Cited by 5 (0 self)
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. When the action of G is free, then S = T is called a quasibundle. In this paper we analyse several numerical properties of standard isotrivial fibrations. In particular we prove that if q(S) ≥ 1 and S is neither ruled nor a quasibundle, then its minimal model b S satisfies K 2 b S ≤ 8χ(O b S) − 2
Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes
 J. COMP. PHYS
, 1981
"... Several numerical schemes for the solution of hyperbolic conservation laws are based on exploiting the information obtained by considering a sequence of Riemann problems. It is argued that in existing schemes much of this information is degraded, and that only certain features of the exact solution ..."
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Cited by 1007 (2 self)
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Several numerical schemes for the solution of hyperbolic conservation laws are based on exploiting the information obtained by considering a sequence of Riemann problems. It is argued that in existing schemes much of this information is degraded, and that only certain features of the exact solution
A Fast Marching Level Set Method for Monotonically Advancing Fronts
 PROC. NAT. ACAD. SCI
, 1995
"... We present a fast marching level set method for monotonically advancing fronts, which leads to an extremely fast scheme for solving the Eikonal equation. Level set methods are numerical techniques for computing the position of propagating fronts. They rely on an initial value partial differential eq ..."
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Cited by 629 (23 self)
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We present a fast marching level set method for monotonically advancing fronts, which leads to an extremely fast scheme for solving the Eikonal equation. Level set methods are numerical techniques for computing the position of propagating fronts. They rely on an initial value partial differential
Guaranteed minimumrank solutions of linear matrix equations via nuclear norm minimization
, 2007
"... The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and collaborative ..."
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Cited by 561 (20 self)
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, and collaborative filtering. Although specific instances can often be solved with specialized algorithms, the general affine rank minimization problem is NPhard, because it contains vector cardinality minimization as a special case. In this paper, we show that if a certain restricted isometry property holds
Closedform solution of absolute orientation using unit quaternions
 J. Opt. Soc. Am. A
, 1987
"... Finding the relationship between two coordinate systems using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task. It finds applications in stereophotogrammetry and in robotics. I present here a closedform solution to the leastsquares pr ..."
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Cited by 990 (4 self)
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squares problem for three or more points. Currently various empirical, graphical, and numerical iterative methods are in use. Derivation of the solution is simplified by use of unit quaternions to represent rotation. I emphasize a symmetry property that a solution to this problem ought to possess. The best
Least angle regression
, 2004
"... The purpose of model selection algorithms such as All Subsets, Forward Selection and Backward Elimination is to choose a linear model on the basis of the same set of data to which the model will be applied. Typically we have available a large collection of possible covariates from which we hope to s ..."
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Cited by 1325 (37 self)
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modification efficiently implements Forward Stagewise linear regression, another promising new model selection method; this connection explains the similar numerical results previously observed for the Lasso and Stagewise, and helps us understand the properties of both methods, which are seen as constrained
Pastry: Scalable, decentralized object location and routing for largescale peertopeer systems,”
 in Proc. of the 18th IFIP/ACM International conference on Distributed Systems Platforms,
, 2001
"... Abstract. This paper presents the design and evaluation of Pastry, a scalable, distributed object location and routing substrate for widearea peertopeer applications. Pastry performs applicationlevel routing and object location in a potentially very large overlay network of nodes connected via ..."
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Cited by 1925 (1 self)
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to the node with a nodeId that is numerically closest to the key, among all currently live Pastry nodes. Each Pastry node keeps track of its immediate neighbors in the nodeId space, and noti£es applications of new node arrivals, node failures and recoveries. Pastry takes into account network locality
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