Results 1  10
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60
Efficiently computing static single assignment form and the control dependence graph
 ACM TRANSACTIONS ON PROGRAMMING LANGUAGES AND SYSTEMS
, 1991
"... In optimizing compilers, data structure choices directly influence the power and efficiency of practical program optimization. A poor choice of data structure can inhibit optimization or slow compilation to the point that advanced optimization features become undesirable. Recently, static single ass ..."
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Cited by 839 (7 self)
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In optimizing compilers, data structure choices directly influence the power and efficiency of practical program optimization. A poor choice of data structure can inhibit optimization or slow compilation to the point that advanced optimization features become undesirable. Recently, static single assignment form and the control dependence graph have been proposed to represent data flow and control flow propertiee of programs. Each of these previously unrelated techniques lends efficiency and power to a useful class of program optimization. Although both of these structures are attractive, the difficulty of their construction and their potential size have discouraged their use. We present new algorithms that efficiently compute these data structures for arbitrary control flow graphs. The algorithms use dominance frontiers, a new concept that may have other applications. We also give analytical and experimental evidence that all of these data structures are usually linear in the size of the original program. This paper thus presents strong evidence that these structures can be of practical use in optimization.
Pseudozeros of Polynomials and Pseudospectra of Companion Matrices
, 1994
"... this paper we take a geometric view of the conditioning of these two problems and of the stability of algorithms for polynomial zerofinding. The fflpseudozero set Z ffl (p) is the set of zeros of all polynomials p obtained by coefficientwise perturbations of p of size ..."
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Cited by 36 (2 self)
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this paper we take a geometric view of the conditioning of these two problems and of the stability of algorithms for polynomial zerofinding. The fflpseudozero set Z ffl (p) is the set of zeros of all polynomials p obtained by coefficientwise perturbations of p of size
Iterative method for cyclically reduced nonselfadjoint linear systems
 Math. Comput
, 1990
"... Abstract. We study iterative methods for solving linear systems of the type arising from twocyclic discretizations of nonselfadjoint twodimensional elliptic partial differential equations. A prototype is the convectiondiffusion equation. The methods consist of applying one step of cyclic reduct ..."
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Cited by 36 (5 self)
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Abstract. We study iterative methods for solving linear systems of the type arising from twocyclic discretizations of nonselfadjoint twodimensional elliptic partial differential equations. A prototype is the convectiondiffusion equation. The methods consist of applying one step of cyclic reduction, resulting in a "reduced system " of half the order of the original discrete problem, combined with a reordering and a block iterative technique for solving the reduced system. For constantcoefficient problems, we present analytic bounds on the spectral radii of the iteration matrices in terms of cell Reynolds numbers that show the methods to be rapidly convergent. In addition, we describe numerical experiments that supplement the analysis and that indicate that the methods compare favorably with methods for solving the "unreduced " system. 1.
Prospectus for the Development of a Linear Algebra Library for HighPerformance Computers
 MATHEMATICS AND COMPUTER SCIENCE DIVISION REPORT ANL/MCSTM97, ARGONNE NATIONAL LABORATORY, ARGONNE, IL
, 1987
"... ..."
A numerical and theoretical study of certain nonlinear wave phenomena
 Phil. Trans. Roy. Soc. London A
, 1978
"... ..."
A Framework for Symmetric Band Reduction
, 1999
"... this paper, we generalize the ideas behind the RSalgorithms and the MHLalgorithm. We develop a band reduction algorithm that eliminates d subdiagonals of a symmetric banded matrix with semibandwidth b (d < b), in a fashion akin to the MHL tridiagonalization algorithm. Then, like the Rutishauser alg ..."
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Cited by 29 (6 self)
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this paper, we generalize the ideas behind the RSalgorithms and the MHLalgorithm. We develop a band reduction algorithm that eliminates d subdiagonals of a symmetric banded matrix with semibandwidth b (d < b), in a fashion akin to the MHL tridiagonalization algorithm. Then, like the Rutishauser algorithm, the band reduction algorithm is repeatedly used until the reduced matrix is tridiagonal. If d = b 1, it is the MHLalgorithm; and if d = 1 is used for each reduction step, it results in the Rutishauser algorithm. However, d need not be chosen this way; indeed, exploiting the freedom we have in choosing d leads to a class of algorithms for banded reduction and tridiagonalization with favorable computational properties. In particular, we can derive algorithms with
Automatic Generation of DAG Parallelism
 Proceedings of the ACM SIGPLAN 89 Conference on PRogramming Language Design and Implementation
, 1989
"... This paper extends the notion of shared and private ..."
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Cited by 19 (2 self)
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This paper extends the notion of shared and private
Numerical Methods for Algebraic Riccati Equations
 Proc. Workshop on the Riccati Equation in Control, Systems, and Signals
, 1989
"... Linear quadratic optimal control problems and the computation of Kalman filters require numerical solutions of discrete and continuous algebraic Riccati equations. ..."
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Cited by 19 (17 self)
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Linear quadratic optimal control problems and the computation of Kalman filters require numerical solutions of discrete and continuous algebraic Riccati equations.
NumericSymbolic Algorithms for Evaluating OneDimensional Algebraic Sets
 APPEARED IN PROCEEDINGS OF ISSAC'95
, 1995
"... We present efficient algorithms based on a combination of numeric and symbolic techniques for evaluating onedimensional algebraic sets in a subset of the real domain. Given a description of a onedimensional algebraic set, we compute its projection using resultants. We represent the resulting plane ..."
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Cited by 18 (5 self)
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We present efficient algorithms based on a combination of numeric and symbolic techniques for evaluating onedimensional algebraic sets in a subset of the real domain. Given a description of a onedimensional algebraic set, we compute its projection using resultants. We represent the resulting plane curve as a singular set of a matrix polynomial as opposed to roots of a bivariate polynomial. Given the matrix formulation, we make use of algorithms from numerical linear algebra to compute start points on all the components, partition the domain such that each resulting region contains only one component and evaluate it accurately using marching methods. We also present techniques to handle singularities for wellconditioned inputs. The resulting algorithm is iterative and its complexity is output sensitive. It has been implemented in oatingpoint arithmetic and we highlight its performance in the context of computing intersection of highdegree algebraic surfaces.
MultiMATLAB: Integrating MATLAB with HighPerformance Parallel Computing
 In Proceedings of Supercomputing '97
, 1997
"... Matlab is the most popular scientific computing environment available on uniprocessors today. Unfortunately, no such environment is currently available for multiprocessors. MultiMatlab [1] is a general extension of the Matlab environment to any distributed memory multiprocessors. This paper present ..."
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Cited by 14 (1 self)
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Matlab is the most popular scientific computing environment available on uniprocessors today. Unfortunately, no such environment is currently available for multiprocessors. MultiMatlab [1] is a general extension of the Matlab environment to any distributed memory multiprocessors. This paper presents a new MultiMatlab system designed to provide highperformance on multiprocessors while maintaining the functionality and usability of the Matlab environment. This system will enable users to access highperformance parallel routines from within the Matlab environment, to extend the environment with new parallel routines, and to use these routines to develop parallel applications with the Matlab language. We discuss a general MultiMatlab architecture, present two implementations based upon the MPI communication standard [2], and demonstrate the use of this system. Preliminary results indicate that the MultiMatlab system can offer the full performance of the underlying multiprocessor to the ...