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Iterative Decoding
"... Algebra review BCH codes Algebraic codes for Flash 3 Graphbased codes LDPC code construction ..."
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Algebra review BCH codes Algebraic codes for Flash 3 Graphbased codes LDPC code construction
Scaling StepWise Refinement
 IEEE TRANSACTIONS ON SOFTWARE ENGINEERING
, 2004
"... Stepwise refinement is a powerful paradigm for developing a complex program from a simple program by adding features incrementally. We present the AHEAD (Algebraic Hierarchical Equations for Application Design) model that shows how stepwise refinement scales to synthesize multiple programs and mu ..."
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Cited by 454 (41 self)
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Stepwise refinement is a powerful paradigm for developing a complex program from a simple program by adding features incrementally. We present the AHEAD (Algebraic Hierarchical Equations for Application Design) model that shows how stepwise refinement scales to synthesize multiple programs
A review of algebraic multigrid
, 2001
"... Since the early 1990s, there has been a strongly increasing demand for more efficient methods to solve large sparse, unstructured linear systems of equations. For practically relevant problem sizes, classical onelevel methods had already reached their limits and new hierarchical algorithms had to b ..."
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Cited by 347 (11 self)
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to be developed in order to allow an efficient solution of even larger problems. This paper gives a review of the first hierarchical and purely matrixbased approach, algebraic multigrid (AMG). AMG can directly be applied, for instance, to efficiently solve various types of elliptic partial differential equations
A New Efficient Algorithm for Computing Gröbner Bases (F4)
 IN: ISSAC ’02: PROCEEDINGS OF THE 2002 INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION
, 2002
"... This paper introduces a new efficient algorithm for computing Gröbner bases. To avoid as much as possible intermediate computation, the algorithm computes successive truncated Gröbner bases and it replaces the classical polynomial reduction found in the Buchberger algorithm by the simultaneous reduc ..."
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Cited by 365 (57 self)
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reduction of several polynomials. This powerful reduction mechanism is achieved by means of a symbolic precomputation and by extensive use of sparse linear algebra methods. Current techniques in linear algebra used in Computer Algebra are reviewed together with other methods coming from the numerical field
Nested Linear/Lattice Codes for Structured Multiterminal Binning
, 2002
"... Network information theory promises high gains over simple pointtopoint communication techniques, at the cost of higher complexity. However, lack of structured coding schemes limited the practical application of these concepts so far. One of the basic elements of a network code is the binning sch ..."
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Cited by 345 (14 self)
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scheme. Wyner and other researchers proposed various forms of coset codes for efficient binning, yet these schemes were applicable only for lossless source (or noiseless channel) network coding. To extend the algebraic binning approach to lossy source (or noisy channel) network coding, recent work
SecondOrder Cone Programming
 MATHEMATICAL PROGRAMMING
, 2001
"... In this paper we survey the second order cone programming problem (SOCP). First we present several applications of the problem in various areas of engineering and robust optimization problems. We also give examples of optimization problems that can be cast as SOCPs. Next we review an algebraic struc ..."
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Cited by 247 (11 self)
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In this paper we survey the second order cone programming problem (SOCP). First we present several applications of the problem in various areas of engineering and robust optimization problems. We also give examples of optimization problems that can be cast as SOCPs. Next we review an algebraic
On the 'Piano Movers' Problem II. General Techniques for Computing Topological Properties of Real Algebraic Manifolds
, 1982
"... This paper continues the discussion, begun in [SS], of the following problem, which arises in robotics: Given a collection of bodies B, which may be hinged, i.e. may allow internal motion around various joints, and given a region bounded by a collection of polyhedral or other simple walls, decide ..."
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Cited by 228 (9 self)
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of an arbitrary real algebraic variety. Various algorithmic issues concerning computations with algebraic numbers, which are required in the algorithms presented in this paper, are also reviewed.
Ideal Theory of BCHAlgebras 1
"... Abstract: In this paper, we introduce the notions of atoms and some types of ideals in BCHalgebras and we stated and proved some theorems which determine the relationship between these ideals and other ideals of BCHalgebras and by some examples we show that these notions are different. Key words: ..."
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Abstract: In this paper, we introduce the notions of atoms and some types of ideals in BCHalgebras and we stated and proved some theorems which determine the relationship between these ideals and other ideals of BCHalgebras and by some examples we show that these notions are different. Key words
SOME CATEGORICAL ASPECTS OF BCHALGEBRAS
, 2001
"... ... We also show that it has coequalizers, kernel pairs, and an image factorization system. It is also proved that onto homomorphisms and coequalizers, and monomorphisms and onetoone homomorphisms coincide, respectively, in BCH. It is shown that MBCI is a coreflexive subcategory of BCH. Regular ho ..."
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Cited by 2 (1 self)
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... We also show that it has coequalizers, kernel pairs, and an image factorization system. It is also proved that onto homomorphisms and coequalizers, and monomorphisms and onetoone homomorphisms coincide, respectively, in BCH. It is shown that MBCI is a coreflexive subcategory of BCH. Regular
On differential graded categories
 INTERNATIONAL CONGRESS OF MATHEMATICIANS. VOL. II
, 2006
"... Differential graded categories enhance our understanding of triangulated categories appearing in algebra and geometry. In this survey, we review their foundations and report on recent work by Drinfeld, DuggerShipley,..., Toën and ToënVaquié. ..."
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Cited by 190 (4 self)
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Differential graded categories enhance our understanding of triangulated categories appearing in algebra and geometry. In this survey, we review their foundations and report on recent work by Drinfeld, DuggerShipley,..., Toën and ToënVaquié.
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