Formal derivation of algorithms: The triangular sylvester equation
ACM Transactions on Mathematical Software (TOMS)
Numerical parameterization of affine varieties using
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Structured perturbations of group inverse and singular linear system with index one
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Representing linear algebra algorithms in code: the FLAME application program interfaces
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Algebraic analysis of high-pass quantization
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Mixture Models Based on Neural Network Averaging
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Hybrid solvers for composition and splitting methods
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Improving the compensated Horner scheme with a fused multiply and add
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Provably faithful evaluation of polynomials
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Bernstein-Bezoutian matrices and curve implicitization
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Adaptive Strassen's matrix multiplication
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The schur aggregation for solving linear systems of equations
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Null space and eigenspace computations with additive preprocessing
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Minimum converging precision of the QR-factorization algorithm for real polynomial GCD
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Certification of the QR factor R and of lattice basis reducedness
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Block LU factors of generalized companion matrix pencils
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Additive preconditioning and aggregation in matrix computations
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Decomposition of the multi-dimensional time series identification problem
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International Journal of Parallel, Emergent and Distributed Systems
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Time Complexity and Convergence Analysis of Domain Theoretic Picard Method
WoLLIC '08 Proceedings of the 15th international workshop on Logic, Language, Information and Computation
Level-2 condition numbers for least-squares solution of Kronecker product linear systems
International Journal of Computer Mathematics
Numerical stability of nonequispaced fast Fourier transforms
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Schur aggregation for linear systems and determinants
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Rigorous and Efficient Short Lattice Vectors Enumeration
ASIACRYPT '08 Proceedings of the 14th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
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Stochastic perturbations and smooth condition numbers
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Backward errors for eigenproblem of two kinds of structured matrices
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Chebyshev interpolation polynomial-based tools for rigorous computing
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Real and complex polynomial root-finding with eigen-solving and preprocessing
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Properties of and improvements to time-domain dynamic thermal analysis algorithms
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A fast solver for linear systems with displacement structure
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Interval slopes as a numerical abstract domain for floating-point variables
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Validated special functions software
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The Exact Distribution of the Condition Number of a Gaussian Matrix
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An Improved Arc Algorithm for Detecting Definite Hermitian Pairs
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On the Semidefinite B-Arnoldi Method
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A New Scaling and Squaring Algorithm for the Matrix Exponential
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Optimal Conditioning of Bernstein Collocation Matrices
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Partitioned Triangular Tridiagonalization
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Growth factors of pivoting strategies associated with Neville elimination
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Running error for the evaluation of rational Bézier surfaces through a robust algorithm
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New progress in real and complex polynomial root-finding
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Estimating the Backward Error in LSQR
SIAM Journal on Matrix Analysis and Applications
A Posteriori Error Estimates Including Algebraic Error and Stopping Criteria for Iterative Solvers
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A Novel Parallel QR Algorithm for Hybrid Distributed Memory HPC Systems
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Polynomial algebra for Birkhoff interpolants
Numerical Algorithms
Quasi-Monte Carlo methods for elliptic PDEs with random coefficients and applications
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VECPAR'10 Proceedings of the 9th international conference on High performance computing for computational science
Improving accuracy for matrix multiplications on GPUs
Scientific Programming
An LLL-reduction algorithm with quasi-linear time complexity: extended abstract
Proceedings of the forty-third annual ACM symposium on Theory of computing
Randomized preconditioning of the MBA algorithm
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Proofs of numerical programs when the compiler optimizes
Innovations in Systems and Software Engineering
Making NTRU as secure as worst-case problems over ideal lattices
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
Rounding coefficients and artificially underflowing terms in non-numeric expressions
ACM Communications in Computer Algebra
The university of Florida sparse matrix collection
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Bit-size estimates for triangular sets in positive dimension
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Segmented Tau approximation for a forward-backward functional differential equation
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An Augmented Stability Result for the Lanczos Hermitian Matrix Tridiagonalization Process
SIAM Journal on Matrix Analysis and Applications
Accurate Matrix Factorization: Inverse LU and Inverse QR Factorizations
SIAM Journal on Matrix Analysis and Applications
Optimizing Halley's Iteration for Computing the Matrix Polar Decomposition
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Rigorous Perturbation Bounds of Some Matrix Factorizations
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Spectral Condition Numbers of Orthogonal Projections and Full Rank Linear Least Squares Residuals
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Communication-optimal Parallel and Sequential Cholesky Decomposition
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Ergodicity Coefficients Defined by Vector Norms
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Goal-Oriented and Modular Stability Analysis
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On the Numerical Analysis of Oblique Projectors
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Computing Characteristic Polynomials from Eigenvalues
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Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators
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Estimating Computational Noise
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MINRES-QLP: A Krylov Subspace Method for Indefinite or Singular Symmetric Systems
SIAM Journal on Scientific Computing
Lehmann Bounds and Eigenvalue Error Estimation
SIAM Journal on Numerical Analysis
A Sinc Function Analogue of Chebfun
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Estimates of the Norm of the Error in Solving Linear Systems with FOM and GMRES
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LSMR: An Iterative Algorithm for Sparse Least-Squares Problems
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Computing the sign of a dot product sum
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Novel modifications of parallel Jacobi algorithms
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Backward errors and condition numbers of regular and singular points on algebraic curves
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
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Fast verification for respective eigenvalues of symmetric matrix
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
A more accurate Briggs method for the logarithm
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Analysis of an implicitly restarted simpler GMRES variant of augmented GMRES
ICCSA'10 Proceedings of the 2010 international conference on Computational Science and Its Applications - Volume Part II
PerPI: a tool to measure instruction level parallelism
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume Part I
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume 2
Reducing rounding errors and achieving Brouwer's law with Taylor Series Method
Applied Numerical Mathematics
Original article: Computational complexity of iterated maps on the interval
Mathematics and Computers in Simulation
Perturbation analysis for the hyperbolic QR factorization
Computers & Mathematics with Applications
The functions erf and erfc computed with arbitrary precision and explicit error bounds
Information and Computation
Accurate summation, dot product and polynomial evaluation in complex floating point arithmetic
Information and Computation
A robust algorithm for geometric predicate by error-free determinant transformation
Information and Computation
Editors Choice Article: I2VM: Incremental import vector machines
Image and Vision Computing
A dynamic program analysis to find floating-point accuracy problems
Proceedings of the 33rd ACM SIGPLAN conference on Programming Language Design and Implementation
Accurate matrix exponential computation to solve coupled differential models in engineering
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Voxelized Minkowski sum computation on the GPU with robust culling
Computer-Aided Design
Accurate evaluation algorithm for bivariate polynomial in Bernstein-Bézier form
Applied Numerical Mathematics
Communication-optimal parallel algorithm for strassen's matrix multiplication
Proceedings of the twenty-fourth annual ACM symposium on Parallelism in algorithms and architectures
ACM Transactions on Mathematical Software (TOMS)
Refining and verifying the solution of a linear system
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Stable Computation of the CS Decomposition: Simultaneous Bidiagonalization
SIAM Journal on Matrix Analysis and Applications
Verified Bounds for Least Squares Problems and Underdetermined Linear Systems
SIAM Journal on Matrix Analysis and Applications
CALU: A Communication Optimal LU Factorization Algorithm
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Nyström approximate model selection for LSSVM
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Reducing the amount of pivoting in symmetric indefinite systems
PPAM'11 Proceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part I
On significance of the least significant bits for differential privacy
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Stability of Recommendation Algorithms
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Algorithm 924: TIDES, a Taylor Series Integrator for Differential EquationS
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Communication-avoiding parallel strassen: implementation and performance
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Maximum edge-cuts in cubic graphs with large girth and in random cubic graphs
Random Structures & Algorithms
FPGA-specific synthesis of loop-nests with pipelined computational cores
Microprocessors & Microsystems
Compressive sensing based sub-mm accuracy UWB positioning systems: A space-time approach
Digital Signal Processing
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Accurate solution of dense linear systems, Part II: Algorithms using directed rounding
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EuroVis'10 Proceedings of the 12th Eurographics / IEEE - VGTC conference on Visualization
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Exponential Taylor methods: Analysis and implementation
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Expert Systems with Applications: An International Journal
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Computational Statistics & Data Analysis
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Hi-index | 0.04 |
From the Publisher:What is the most accurate way to sum floating point numbers? What are the advantages of IEEE arithmetic? How accurate is Gaussian elimination and what were the key breakthroughs in the development of error analysis for the method? The answers to these and many related questions are included here. This book gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory, and rounding error analysis. Software practicalities are emphasized throughout, with particular reference to LAPACK and MATLAB. The best available error bounds, some of them new, are presented in a unified format with a minimum of jargon. Because of its central role in revealing problem sensitivity and providing error bounds, perturbation theory is treated in detail. Historical perspective and insight are given, with particular reference to the fundamental work of Wilkinson and Turing, and the many quotations provide further information in an accessible format. The book is unique in that algorithmic developments and motivations are given succinctly and implementation details minimized, so that attention can be concentrated on accuracy and stability results. Here, in one place and in a unified notation, is error analysis for most of the standard algorithms in matrix computations. Not since Wilkinson's Rounding Errors in Algebraic Processes (1963) and The Algebraic Eigenvalue Problem (1965) has any volume treated this subject in such depth. A number of topics are treated that are not usually covered in numerical analysis textbooks, including floating point summation, block LU factorization, condition number estimation, the Sylvester equation, powers of matrices, finite precision behavior of stationary iterative methods, Vandermonde systems, and fast matrix multiplication. Although not designed specifically as a textbook, this volume is a suitable reference for an advanced course, and could be used by instructors at all levels as a supplementary text from which to draw examples, historical perspective, statements of results, and exercises (many of which have never before appeared in textbooks). The book is designed to be a comprehensive reference and its bibliography contains more than 1100 references from the research literature. Audience Specialists in numerical analysis as well as computational scientists and engineers concerned about the accuracy of their results will benefit from this book. Much of the book can be understood with only a basic grounding in numerical analysis and linear algebra. About the Author Nicholas J. Higham is a Professor of Applied Mathematics at the University of Manchester, England. He is the author of more than 40 publications and is a member of the editorial boards of the SIAM Journal on Matrix Analysis and Applications and the IMA Journal of Numerical Analysis. His book Handbook of Writing for the Mathematical Sciences was published by SIAM in 1993.