The Experts below are selected from a list of 12183 Experts worldwide ranked by ideXlab platform
Yue Yang - One of the best experts on this subject based on the ideXlab platform.
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Path-sensitive dataflow analysis with Iterative Refinement
Lecture Notes in Computer Science, 2006Co-Authors: Dinakar Dhurjati, Manuvir Das, Yue YangAbstract:In this paper, we present a new method for supporting abstraction Refinement in path-sensitive dataflow analysis. We show how an adjustable merge criterion can be used as an interface to control the degree of abstraction. In particular, we partition the merge criterion with two sets of predicates - one related to the dataflow facts being propagated and the other related to path feasibility. These tracked predicates are then used to guide merge operations and path feasibility analysis, so that expensive computations are performed only at the right places. Refinement amounts to lazily growing the path predicate set to recover lost precision. We have implemented our Refinement technique in ESP, a software validation tool for C/C++ programs. We apply ESP to validate a future version of Windows against critical security properties. Our experience suggests that applying Iterative Refinement to path-sensitive dataflow analysis is both effective in cutting down spurious errors and scalable enough for solving real world problems.
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SAS - Path-Sensitive dataflow analysis with Iterative Refinement
Static Analysis, 2006Co-Authors: Dinakar Dhurjati, Manuvir Das, Yue YangAbstract:In this paper, we present a new method for supporting abstraction Refinement in path-sensitive dataflow analysis. We show how an adjustable merge criterion can be used as an interface to control the degree of abstraction. In particular, we partition the merge criterion with two sets of predicates — one related to the dataflow facts being propagated and the other related to path feasibility. These tracked predicates are then used to guide merge operations and path feasibility analysis, so that expensive computations are performed only at the right places. Refinement amounts to lazily growing the path predicate set to recover lost precision. We have implemented our Refinement technique in ESP, a software validation tool for C/C++ programs. We apply ESP to validate a future version of Windows against critical security properties. Our experience suggests that applying Iterative Refinement to path-sensitive dataflow analysis is both effective in cutting down spurious errors and scalable enough for solving real world problems.
Andrés E. Tomás - One of the best experts on this subject based on the ideXlab platform.
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ISC Workshops - Residual Replacement in Mixed-Precision Iterative Refinement for Sparse Linear Systems
Lecture Notes in Computer Science, 2018Co-Authors: Hartwig Anzt, Goran Flegar, Vedran Novaković, Enrique S. Quintana-ortí, Andrés E. TomásAbstract:We investigate the solution of sparse linear systems via Iterative methods based on Krylov subspaces. Concretely, we combine the use of extended precision in the outer Iterative Refinement with a reduced precision in the inner Conjugate Gradient solver. This method is additionally enhanced with different residual replacement strategies that aim to avoid the pitfalls due to the divergence between the actual residual and the recurrence formula for this parameter computed during the iteration. Our experiments using a significant part of the SuiteSparse Matrix Collection illustrate the potential benefits of this technique from the point of view, for example, of energy and performance.
Francisco J Quiles - One of the best experts on this subject based on the ideXlab platform.
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an Iterative Refinement technique for side information generation in dvc
International Conference on Multimedia and Expo, 2007Co-Authors: W A R J Weerakkody, W A C Fernando, Jose Luis Martinez, Pedro Cuenca, Francisco J QuilesAbstract:Distributed video coding (DVC) is an increasingly popular approach among the researchers in video coding during past few years due to its attractive and promising features. In DVC, the majority of the computational complexity has been shifted from encoder to the decoder in comparison to its conventional counterparts, including MPEG and H.26 x enabling a dramatically low cost encoder implementation. Side information generation, carried out at the decoder, is a major function in the DVC coding algorithm and plays a key-role in determining the performance of the codec. In this paper, a novel Iterative Refinement technique is proposed for the side information generation process. Simulation results of the proposed technique depict a consistent improvement in performance in comparison to the state-of-the-art in pixel domain DVC.
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ICME - An Iterative Refinement Technique for Side Information Generation in DVC
Multimedia and Expo 2007 IEEE International Conference on, 2007Co-Authors: W A R J Weerakkody, W A C Fernando, Jose Luis Martinez, Pedro Cuenca, Francisco J QuilesAbstract:Distributed video coding (DVC) is an increasingly popular approach among the researchers in video coding during past few years due to its attractive and promising features. In DVC, the majority of the computational complexity has been shifted from encoder to the decoder in comparison to its conventional counterparts, including MPEG and H.26 x enabling a dramatically low cost encoder implementation. Side information generation, carried out at the decoder, is a major function in the DVC coding algorithm and plays a key-role in determining the performance of the codec. In this paper, a novel Iterative Refinement technique is proposed for the side information generation process. Simulation results of the proposed technique depict a consistent improvement in performance in comparison to the state-of-the-art in pixel domain DVC.
Dinakar Dhurjati - One of the best experts on this subject based on the ideXlab platform.
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Path-sensitive dataflow analysis with Iterative Refinement
Lecture Notes in Computer Science, 2006Co-Authors: Dinakar Dhurjati, Manuvir Das, Yue YangAbstract:In this paper, we present a new method for supporting abstraction Refinement in path-sensitive dataflow analysis. We show how an adjustable merge criterion can be used as an interface to control the degree of abstraction. In particular, we partition the merge criterion with two sets of predicates - one related to the dataflow facts being propagated and the other related to path feasibility. These tracked predicates are then used to guide merge operations and path feasibility analysis, so that expensive computations are performed only at the right places. Refinement amounts to lazily growing the path predicate set to recover lost precision. We have implemented our Refinement technique in ESP, a software validation tool for C/C++ programs. We apply ESP to validate a future version of Windows against critical security properties. Our experience suggests that applying Iterative Refinement to path-sensitive dataflow analysis is both effective in cutting down spurious errors and scalable enough for solving real world problems.
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SAS - Path-Sensitive dataflow analysis with Iterative Refinement
Static Analysis, 2006Co-Authors: Dinakar Dhurjati, Manuvir Das, Yue YangAbstract:In this paper, we present a new method for supporting abstraction Refinement in path-sensitive dataflow analysis. We show how an adjustable merge criterion can be used as an interface to control the degree of abstraction. In particular, we partition the merge criterion with two sets of predicates — one related to the dataflow facts being propagated and the other related to path feasibility. These tracked predicates are then used to guide merge operations and path feasibility analysis, so that expensive computations are performed only at the right places. Refinement amounts to lazily growing the path predicate set to recover lost precision. We have implemented our Refinement technique in ESP, a software validation tool for C/C++ programs. We apply ESP to validate a future version of Windows against critical security properties. Our experience suggests that applying Iterative Refinement to path-sensitive dataflow analysis is both effective in cutting down spurious errors and scalable enough for solving real world problems.
Nicholas J. Higham - One of the best experts on this subject based on the ideXlab platform.
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Three-Precision GMRES-Based Iterative Refinement for Least Squares Problems
SIAM Journal on Scientific Computing, 2020Co-Authors: Erin Carson, Nicholas J. Higham, Srikara PraneshAbstract:The standard Iterative Refinement procedure for improving an approximate solution to the least squares problem $\min_x\|b - Ax\|_2$, where $A\in\mathbb{R}^{m\times n}$ with $m \ge n$ has full rank,...
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accelerating the solution of linear systems by Iterative Refinement in three precisions
SIAM Journal on Scientific Computing, 2018Co-Authors: Erin Carson, Nicholas J. HighamAbstract:We propose a general algorithm for solving a $n\times n$ nonsingular linear system $Ax = b$ based on Iterative Refinement with three precisions. The working precision is combined with possibly different precisions for solving for the correction term and for computing the residuals. Via rounding error analysis of the algorithm we derive sufficient conditions for convergence and bounds for the attainable normwise forward error and normwise and componentwise backward errors. Our results generalize and unify many existing rounding error analyses for Iterative Refinement. With single precision as the working precision, we show that by using LU factorization in IEEE half precision as the solver and calculating the residuals in double precision it is possible to solve $Ax = b$ to full single precision accuracy for condition numbers $\kappa_2(A) \le 10^4$, with the $O(n^3)$ part of the computations carried out entirely in half precision. We show further that by solving the correction equations by GMRES preconditioned by the LU factors the restriction on the condition number can be weakened to $\kappa_2(A) \le 10^8$, although in general there is no guarantee that GMRES will converge quickly. Taking for comparison a standard $Ax = b$ solver that uses LU factorization in single precision, these results suggest that on architectures for which half precision is efficiently implemented it will be possible to solve certain linear systems $Ax = b$ up to twice as fast \emph{and} to greater accuracy. Analogous results are given with double precision as the working precision.
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a new analysis of Iterative Refinement and its application to accurate solution of ill conditioned sparse linear systems
SIAM Journal on Scientific Computing, 2017Co-Authors: Erin Carson, Nicholas J. HighamAbstract:Iterative Refinement is a long-standing technique for improving the accuracy of a computed solution to a nonsingular linear system $Ax = b$ obtained via LU factorization. It makes use of residuals computed in extra precision, typically at twice the working precision, and existing results guarantee convergence if the matrix $A$ has condition number safely less than the reciprocal of the unit roundoff, $u$. We identify a mechanism that allows Iterative Refinement to produce solutions with normwise relative error of order $u$ to systems with condition numbers of order $u^{-1}$ or larger, provided that the update equation is solved with a relative error sufficiently less than $1$. A new rounding error analysis is given and its implications are analyzed. Building on the analysis, we develop a GMRES-based Iterative Refinement method (GMRES-IR) that makes use of the computed LU factors as preconditioners. GMRES-IR exploits the fact that even if $A$ is extremely ill conditioned the LU factors contain enough information that preconditioning can greatly reduce the condition number of $A$. Our rounding error analysis and numerical experiments show that GMRES-IR can succeed where standard Refinement fails, and that it can provide accurate solutions to systems with condition numbers of order $u^{-1}$ and greater. Indeed in our experiments with such matrices---both random and from the University of Florida Sparse Matrix Collection---GMRES-IR yields a normwise relative error of order $u$ in at most $3$ steps in every case.
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Iterative Refinement for linear systems and LAPACK
IMA Journal of Numerical Analysis, 1997Co-Authors: Nicholas J. HighamAbstract:The technique of Iterative Refinement for improving the computed solution to a linear system was used on desk calculators and computers in the 1940s and has remained popular. In the 1990s Iterative Refinement is well supported in software libraries, notably in LAPACK. Although the behaviour of Iterative Refinement in floating point arithmetic is reasonably well understood, the existing theory is not sufficient to justify the use of fixed precision Iterative Refinement in all the LAPACK routines in which it is implemented. We present analysis that provides the theoretical support needed for LAPACK. The analysis covers both mixed and fixed precision Iterative Refinement with an arbitrary number of iterations, makes only a general assumption on the underlying solver, and is relatively short. We identify some remaining open problems.
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Iterative Refinement enhances the stability of qr factorization methods for solving linear equations
Bit Numerical Mathematics, 1991Co-Authors: Nicholas J. HighamAbstract:Iterative Refinement is a well-known technique for improving the quality of an approximate solution to a linear system. In the traditional usage residuals are computed in extended precision, but more recent work has shown that fixed precision is sufficient to yield benefits for stability. We extend existing results to show that fixed precision Iterative Refinement renders anarbitrary linear equations solver backward stable in a strong, componentwise sense, under suitable assumptions. Two particular applications involving theQR factorization are discussed in detail: solution of square linear systems and solution of least squares problems. In the former case we show that one step of Iterative Refinement suffices to produce a small componentwise relative backward error. Our results are weaker for the least squares problem, but again we find that Iterative Refinement improves a componentwise measure of backward stability. In particular, Iterative Refinement mitigates the effect of poor row scaling of the coefficient matrix, and so provides an alternative to the use of row interchanges in the HouseholderQR factorization. A further application of the results is described to fast methods for solving Vandermonde-like systems.
