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Parallel arithmetic computations: A survey
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
inferredcites →https://doi.org/10.1007/3-540-16766-8_21openalex-snapshot
Efficient parallel evaluation of straight-line code and arithmetic circuits
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Factoring polynomials with rational coefficients
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Fast parallel calculation of the rank of matrices over a field of arbitrary characteristic
inferredcites →https://doi.org/10.1016/0001-8708(82)90048-2openalex-snapshot
The complexity of the word problems for commutative semigroups and polynomial ideals
inferredcites →https://doi.org/10.1016/0020-0190(80)90033-2openalex-snapshot
Computing multivariate polynomials in parallel
inferredcites →https://doi.org/10.1016/0020-0190(80)90042-3openalex-snapshot
A note on the parallel complexity of computing the rank of order n matrices
inferredcites →https://doi.org/10.1016/0020-0190(84)90018-8openalex-snapshot
On computing the determinant in small parallel time using a small number of processors
inferredcites →https://doi.org/10.1016/0022-0000(85)90043-1openalex-snapshot
Irreducibility of multivariate polynomials
inferredcites →https://doi.org/10.1016/0022-0000(86)90029-2openalex-snapshot
The complexity of elementary algebra and geometry
inferredcites →https://doi.org/10.1016/0885-064x(86)90001-4openalex-snapshot
Polynomial division and its computational complexity
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Perspectives in Mathematics
inferredcites →https://doi.org/10.1016/b978-0-12-592101-5.50006-3openalex-snapshot
A Guide to Parallel Computation and Some Cray-1 Experiences
inferredcites →https://doi.org/10.1016/s0019-9958(82)90766-5openalex-snapshot
Fast parallel matrix and GCD computations
inferredcites →https://doi.org/10.1016/s0019-9958(85)80041-3openalex-snapshot
A taxonomy of problems with fast parallel algorithms
inferredcites →https://doi.org/10.1016/s0747-7171(85)80029-8openalex-snapshot
Fast parallel absolute irreducibility testing
inferredcites →https://doi.org/10.1109/sfcs.1983.29openalex-snapshot
Logarithmic depth circuits for algebraic functions
inferredcites →https://doi.org/10.1109/sfcs.1984.715897openalex-snapshot
Very Fast Parallel Matrix and Polynomial Arithmetic
inferredcites →https://doi.org/10.1137/0205040openalex-snapshot
Fast Parallel Matrix Inversion Algorithms
inferredcites →https://doi.org/10.1137/0206054openalex-snapshot
On Relating Time and Space to Size and Depth
inferredcites →https://doi.org/10.1137/0208010openalex-snapshot
On the Parallel Evaluation of Multivariate Polynomials
inferredcites →https://doi.org/10.1137/0212001openalex-snapshot
The Computational Complexity of Continued Fractions
inferredcites →https://doi.org/10.1137/0212043openalex-snapshot
Fast Parallel Computation of Polynomials Using Few Processors
inferredcites →https://doi.org/10.1137/0213019openalex-snapshot
Parallel Solution of Certain Toeplitz Linear Systems
inferredcites →https://doi.org/10.1137/0213050openalex-snapshot
Parallel Algorithms for Algebraic Problems
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Logarithmic Depth Circuits for Algebraic Functions
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Representations and Parallel Computations for Rational Functions
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Fast Parallel Computation of Hermite and Smith Forms of Polynomial Matrices
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Uniform closure properties of P-computable functions
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A fast parallel algorithm for determining all roots of a polynomial with real roots
inferredcites →https://doi.org/10.1145/22145.22150openalex-snapshot
The parallel complexity of exponentiating polynomials over finite fields
inferredcites →https://doi.org/10.1145/321812.321815openalex-snapshot
The Parallel Evaluation of General Arithmetic Expressions
inferredcites →https://doi.org/10.1145/321941.321945openalex-snapshot
New Algorithms and Lower Bounds for the Parallel Evaluation of Certain Rational Expressions and Recurrences
inferredcites →https://doi.org/10.1145/321958.321973openalex-snapshot
Restructuring of Arithmetic Expressions For Parallel Evaluation
inferredcites →https://doi.org/10.1145/32439.32452openalex-snapshot
Fast parallel algorithms for similarity of matrices
inferredcites →https://doi.org/10.1145/3749740.3749750openalex-snapshot
Completeness Classes in Algebra
inferredcites →https://doi.org/10.1145/800057.808712openalex-snapshot
The complexity of elementary algebra and geometry
inferredcites →https://doi.org/10.1145/800061.808735openalex-snapshot
Lower bounds for algebraic computation trees
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
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On Parallel Complexity of Nonsmooth Convex Optimization
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Nearly Sharp Complexity Bounds for Multiprocessor Algebraic Computations
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On the Parallel Complexity of the Polynomial Ideal Membership Problem
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Deformation Techniques for Efficient Polynomial Equation Solving
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A Gröbner Free Alternative for Polynomial System Solving
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The Projective Noether Maple Package: Computing the Dimension of a Projective Variety
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Circuits versus Trees in Algebraic Complexity
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Polynomial and Rational Evaluation and Interpolation (with Structured Matrices) ⋆
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Parallel algorithms and architectures
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Geometric problems solvable in single exponential time
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Single exponential path finding in semialgebraic sets Part I: The case of a regular bounded hypersurface
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Two P-complete problems in the theory of the reals
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Complexity of the computation of the canonical Whitney stratification of an algebraic set in Cn
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Repeated matrix squaring for the parallel solution of linear systems
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Parallel computations with algebraic numbers a case study: Jordan normal form of matrices
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When polynomial equation systems can be “solved” fast?
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How lower and upper complexity bounds meet in elimination theory
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Regular versus irregular problems and algorithms
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Algorithmes – disons rapides – pour la décomposition d’une variété algébrique en composantes irréductibles et équidimensionnelles
inferred← citeshttps://doi.org/10.1007/978-1-4612-0441-1_13openalex-snapshot
Membership problem, Representation problem and the Computation of the Radical for one-dimensional Ideals
inferred← citeshttps://doi.org/10.1007/978-1-4612-0441-1_6openalex-snapshot
Duality methods for the membership problem
inferred← citeshttps://doi.org/10.1007/978-1-4612-2628-4_28openalex-snapshot
Single Exponential Path Finding in Semi-algebraic Sets, Part II: The General Case
inferred← citeshttps://doi.org/10.1007/978-3-0348-9144-8_12openalex-snapshot
Fast and Efficient Parallel Inversion of Toeplitz and Block Toeplitz Matrices
inferred← citeshttps://doi.org/10.1007/978-3-540-24587-2_64openalex-snapshot
Counting Complexity Classes over the Reals I: The Additive Case
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VC Dimension Bounds for Analytic Algebraic Computations
inferred← citeshttps://doi.org/10.1007/978-3-540-75225-7_12openalex-snapshot
Vapnik-Chervonenkis Dimension of Parallel Arithmetic Computations
inferred← citeshttps://doi.org/10.1007/978-3-642-13411-1_5openalex-snapshot
An Efficient Algorithm for the Sign Condition Problem in the Semi-algebraic Context
inferred← citeshttps://doi.org/10.1007/978-3-662-02851-3_1openalex-snapshot
Computability and Complexity of Polynomial Optimization Problems
inferred← citeshttps://doi.org/10.1007/bf01200406openalex-snapshot
Algorithmic aspects of Suslin's proof of Serre's conjecture
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On the efficiency of effective Nullstellens�tze
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Lower bounds for arithmetic networks
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NC algorithms for real algebraic numbers
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Lower bounds for arithmetic networks II: Sum of Betti numbers
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Effective Łojasiewicz inequalities in semialgebraic geometry
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Description of the connected components of a semialgebraic set in single exponential time
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Parallel models of computation: an introductory survey
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Matrix structures in parallel matrix computations
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Computing large polynomial powers very fast in parallel
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Polar varieties and efficient real elimination
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The Complexity of Stratification Computation
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Robust Algorithms For Generalized Pham Systems
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Counting Irreducible Components of Complex Algebraic Varieties
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Topological lower bounds for arithmetic networks
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Decision problem for a class of univariate Pfaffian functions
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On the Time-Space Complexity of Geometric Elimination Procedures
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Probabilistic Algorithms for Geometric Elimination
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The rate of convergence of Toeplitz based PCG methods for second order nonlinear boundary value problems
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On Sign Conditions Over Real Multivariate Polynomials
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The Hardness of Polynomial Equation Solving
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Deformation Techniques for Sparse Systems
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Algorithms of Intrinsic Complexity for Point Searching in Compact Real Singular Hypersurfaces
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Castelnuovo–Mumford Regularity and Computing the de Rham Cohomology of Smooth Projective Varieties
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Quadratic Newton Iteration for Systems with Multiplicity
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On the Vapnik-Chervonenkis dimension of computer programs which use transcendental elementary operations
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Parallel restructuring and evaluation of expressions
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Precise sequential and parallel complexity bounds for quantifier elimination over algebraically closed fields
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The membership problem for unmixed polynomial ideals is solvable in single exponential time
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Generalised matrix inversion and rank computation by successive matrix powering
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Factoring polynomials and primitive elements for special primes
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Oracle computations in parallel numerical linear algebra
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Parallel information-based complexity
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Matrix inversion in RNC1
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Two P-complete problems in the theory of the reals
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Planar acyclic computation
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Boolean circuits versus arithmetic circuits
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Highly parallel computations modulo a number having only small prime factors
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Parallel algebraic reductions among numerical problems
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Fast and efficient parallel evaluation of the zeros of a polynomial having only real zeros
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Parametrization of Newton's iteration for computations with structured matrices and applications
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Parallel Algorithms for Shared-Memory Machines
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A parametric representation of totally mixed Nash equilibria
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Zero counting for a class of univariate Pfaffian functions
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Numeric vs. symbolic homotopy algorithms in polynomial system solving: a case study
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On the complexity of the resolvent representation of some prime differential ideals
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Computing generators of the ideal of a smooth affine algebraic variety
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Computing multihomogeneous resultants using straight-line programs
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On the complexity of counting components of algebraic varieties
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Polynomial equation solving by lifting procedures for ramified fibers
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Computing bases of complete intersection rings in Noether position
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Effective equidimensional decomposition of affine varieties
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Straight-line programs in geometric elimination theory
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An effective algorithm for quantifier elimination over algebraically closed fields using straight line programs
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On the data structure straight-line program and its implementation in symbolic computation
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Functional decomposition ofpolynomials: the tame case
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Inversion in finite fields using logarithmic depth
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Feasible arithmetic computations: Valiant's hypothesis
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Kronecker's smart, little black boxes
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Polar, bipolar and copolar varieties: Real solving of algebraic varieties with intrinsic complexity
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Fast computation of a rational point of a variety over a finite field
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Point searching in real singularcomplete intersection varieties: algorithms of intrinsic complexity
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Functional decomposition of polynomials
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GPU Tensor Cores for Fast Arithmetic Reductions
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Very Fast Parallel Polynomial Arithmetic
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Constant-Depth Arithmetic Circuits for Linear Algebra Problems
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Counting Complexity Classes for Numeric Computations I: Semilinear Sets
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Nearly Optimal Algorithms for Canonical Matrix Forms
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Parallel Complexity of Computations with General and Toeplitz-Like Matrices Filled with Integers and Extensions
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Differential forms in computational algebraic geometry
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Fast parallel computation of the Smith normal form of polynomial matrices
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Computing an equidimensional decomposition of an algebraic variety by means of geometric resolutions
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Polynomial-Time PIT from (Almost) Necessary Assumptions
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Greatest common divisors of polynomials given by straight-line programs
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Sur la complexité du principe de Tarski-Seidenberg
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Some Results on the Functional Decomposition of Polynomials
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Bases standard, élimination et complexité
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