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The accuracy of solutions to triangular systems
 SIAM J. Numer. Anal
, 1989
"... Abstract. Triangular systems play a fundamental role in matrix computations. It has been prominently stated in the literature, but is perhaps not widely appreciated, that solutions to triangular systems are usually computed to high accuracyhigher than the traditional condition numbers for linear s ..."
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Cited by 14 (6 self)
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Abstract. Triangular systems play a fundamental role in matrix computations. It has been prominently stated in the literature, but is perhaps not widely appreciated, that solutions to triangular systems are usually computed to high accuracyhigher than the traditional condition numbers for linear
Sparse Triangular System Partitioning
"... . The parallel solution of a sparse triangular system can be a serious bottleneck in parallel computation. An improvement on the parallel efficiency can be achieved by partially inverting the triangular system. To this end, the triangular matrix is represented by the product of a (small) number of s ..."
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. The parallel solution of a sparse triangular system can be a serious bottleneck in parallel computation. An improvement on the parallel efficiency can be achieved by partially inverting the triangular system. To this end, the triangular matrix is represented by the product of a (small) number
Adaptive triangular system solving
 In Challenges in Symbolic Computation Software
, 2006
"... Abstract. We propose a new adaptive algorithm for the exact simultaneous resolution of several triangular systems over finite fields: it is composed of several practicable variants solving these systems (a pure recursive version, a reduction to the numerical dtrsm routine and a delaying of the modul ..."
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Cited by 3 (2 self)
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Abstract. We propose a new adaptive algorithm for the exact simultaneous resolution of several triangular systems over finite fields: it is composed of several practicable variants solving these systems (a pure recursive version, a reduction to the numerical dtrsm routine and a delaying
Constraint Hierarchies as Triangular Systems
 Dept of Numerical Analysis and Computing Science, Royal Institute of Technology
, 1991
"... Constraint hierarchies where each constraint is an equation, are considered in this report. Each of the equations is labelled with a preference so that one is able to allow inconsistent equations to be included in such a hierarchy. Such constraint hierarchies are treated as triangular systems, where ..."
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Cited by 2 (0 self)
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Constraint hierarchies where each constraint is an equation, are considered in this report. Each of the equations is labelled with a preference so that one is able to allow inconsistent equations to be included in such a hierarchy. Such constraint hierarchies are treated as triangular systems
Triangular systems for symmetric . . .
, 2009
"... We introduce and study distributions of sets of binary variables that are symmetric, that is each has equally probable levels. The joint distribution of these special types of binary variables, if generated by a recursive process of linear main effects is essentially parametrized in terms of margi ..."
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We introduce and study distributions of sets of binary variables that are symmetric, that is each has equally probable levels. The joint distribution of these special types of binary variables, if generated by a recursive process of linear main effects is essentially parametrized in terms of marginal correlations. This contrasts with the loglinear formulation of joint probabilities in which parameters measure conditional associations given all remaining variables. The new formulation permits useful comparisons of different types of graphical Markov models and leads to a close approximation of Gaussian orthant probabilities.
Triangular systems and factorized Gröbner bases
 IN PROC. AAECC11, VOLUME 948 OF LECT. NOTES COMP. SCI
, 1995
"... Solving systems of polynomial equations in an ultimate way means to nd the isolated primes of the associated variety and to present them in a way that is well suited for further computations. [5] proposes an algorithm, that uses several Gröbner basis computations for a dimension reduction argument, ..."
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Cited by 6 (4 self)
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and constraint inequalities, available in all major computer algebra systems. In a preceding paper [9] we reported on some experience with a new version of this algorithm, implemented in our REDUCE package CALI [8]. Here we discuss, how this approach may be re ned to produce triangular systems in the sense
A BiHamiltonian Formulation for Triangular Systems by Perturbations
, 2001
"... A biHamiltonian formulation is proposed for triangular systems resulted by perturbations around solutions, from which infinitely many symmetries and conserved functionals of triangular systems can be explicitly constructed, provided that one operator of the Hamiltonian pair is invertible. Through o ..."
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Cited by 3 (3 self)
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A biHamiltonian formulation is proposed for triangular systems resulted by perturbations around solutions, from which infinitely many symmetries and conserved functionals of triangular systems can be explicitly constructed, provided that one operator of the Hamiltonian pair is invertible. Through
Triangular systems for symmetric binary variables
 Electr. J. Statist
, 2009
"... Abstract We introduce and study distributions of sets of binary variables that are symmetric, that is each has equally probable levels. The joint distribution of these special types of binary variables, if generated by a recursive process of linear main effects is essentially parametrized in terms ..."
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Cited by 12 (8 self)
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Abstract We introduce and study distributions of sets of binary variables that are symmetric, that is each has equally probable levels. The joint distribution of these special types of binary variables, if generated by a recursive process of linear main effects is essentially parametrized in terms of marginal correlations. This contrasts with the loglinear formulation of joint probabilities in which parameters measure conditional associations given all remaining variables. The new formulation permits useful comparisons of different types of graphical Markov models and leads to a close approximation of Gaussian orthant probabilities.
Stability of parallel triangular system solvers
 SIAM J. Sci. Comput
, 1995
"... And by contacting: ..."
Results 1  10
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197,077