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4,259
ALGEBRAIC ALGORITHMS1
, 2012
"... This is a preliminary version of a Chapter on Algebraic Algorithms in the up ..."
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This is a preliminary version of a Chapter on Algebraic Algorithms in the up
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 653 (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
Direct least Square Fitting of Ellipses
, 1998
"... This work presents a new efficient method for fitting ellipses to scattered data. Previous algorithms either fitted general conics or were computationally expensive. By minimizing the algebraic distance subject to the constraint 4ac  b² = 1 the new method incorporates the ellipticity constraint ..."
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Cited by 430 (3 self)
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This work presents a new efficient method for fitting ellipses to scattered data. Previous algorithms either fitted general conics or were computationally expensive. By minimizing the algebraic distance subject to the constraint 4ac  b² = 1 the new method incorporates the ellipticity constraint
Improved Decoding of ReedSolomon and AlgebraicGeometry Codes
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1999
"... Given an errorcorrecting code over strings of length n and an arbitrary input string also of length n, the list decoding problem is that of finding all codewords within a specified Hamming distance from the input string. We present an improved list decoding algorithm for decoding ReedSolomon codes ..."
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Cited by 345 (44 self)
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Given an errorcorrecting code over strings of length n and an arbitrary input string also of length n, the list decoding problem is that of finding all codewords within a specified Hamming distance from the input string. We present an improved list decoding algorithm for decoding Reed
Accelerated Image Reconstruction using Ordered Subsets of Projection Data
 IEEE TRANS. MED. IMAG
, 1994
"... We define ordered subset processing for standard algorithms (such as Expectation Maximization, EM) for image restoration from projections. Ordered subsets methods group projection data into an ordered sequence of subsets (or blocks). An iteration of ordered subsets EM is defined as a single pass thr ..."
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Cited by 301 (2 self)
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) and multiplicative algebraic reconstruction (MART) techniques are well known special cases. Ordered subsets EM (OSEM) provides a restoration imposing a natural positivity condition and with close links to the EM algorithm. OSEM is applicable in both single photon (SPECT) and positron emission tomography (PET
Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit
, 2006
"... Finding the sparsest solution to underdetermined systems of linear equations y = Φx is NPhard in general. We show here that for systems with ‘typical’/‘random ’ Φ, a good approximation to the sparsest solution is obtained by applying a fixed number of standard operations from linear algebra. Our pr ..."
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Cited by 274 (22 self)
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Finding the sparsest solution to underdetermined systems of linear equations y = Φx is NPhard in general. We show here that for systems with ‘typical’/‘random ’ Φ, a good approximation to the sparsest solution is obtained by applying a fixed number of standard operations from linear algebra. Our
A Factorization Based Algorithm for MultiImage Projective Structure and Motion
, 1996
"... . We propose a method for the recovery of projective shape and motion from multiple images of a scene by the factorization of a matrix containing the images of all points in all views. This factorization is only possible when the image points are correctly scaled. The major technical contribution of ..."
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Cited by 267 (15 self)
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of this paper is a practical method for the recovery of these scalings, using only fundamental matrices and epipoles estimated from the image data. The resulting projective reconstruction algorithm runs quickly and provides accurate reconstructions. Results are presented for simulated and real images. 1
Hecke algebras at roots of unity and crystal bases of quantum affine algebras
, 1995
"... We present a fast algorithm for computing the global crystal basis of the basic Uq(bsln)module. This algorithm is based on combinatorial techniques which have been developed for dealing with modular representations of symmetric groups, and more generally with representations of Hecke algebras of ty ..."
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Cited by 164 (17 self)
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of type A at roots of unity. We conjecture that, upon specialization q! 1, our algorithm computes the decomposition matrices of all Hecke algebras at a nth root of 1.
Solution of systems of linear equations by minimized iterations
 J. Res. Natl. Bur. Stand
, 1952
"... A simple algorithm is described which is well adapted to the effective solution of large systems of linear algebraic equations by a succession of wellconvergent approximations. 1. ..."
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Cited by 214 (0 self)
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A simple algorithm is described which is well adapted to the effective solution of large systems of linear algebraic equations by a succession of wellconvergent approximations. 1.
Some Algebraic and Geometric Computations in PSPACE
, 1988
"... We give a PSPACE algorithm for determining the signs of multivariate polynomials at the common zeros of a system of polynomial equations. One of the consequences of this result is that the “Generalized Movers ’ Problem ” in robotics drops from EXPTIME into PSPACE, and is therefore PSPACEcomplete ..."
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Cited by 168 (2 self)
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combines t1.e tl;eorem of the primitive element from classical algebra with a symbolic polynomial evaluation lemma from [BKR]. A decision problem involving several algrtbraic IIUIII~W~S is rctl~~c~d to a problem involving a siuglc illgel)rilic u~tt~ber or pritnit.ive clement, which rationally grueratrs
Results 1  10
of
4,259