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ACM Transactions on Mathematical Software (TOMS)
CALYPSO: a computer algebra library for parallel symbolic computation
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STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Recursive array layouts and fast parallel matrix multiplication
Proceedings of the eleventh annual ACM symposium on Parallel algorithms and architectures
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IEEE Transactions on Computers
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Conditioning of Pseudospectral Matrices for Certain Domain Decompositions
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A recursive formulation of Cholesky factorization of a matrix in packed storage
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On computational properties of chains of recurrences
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IEEE/ACM Transactions on Networking (TON)
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SC '98 Proceedings of the 1998 ACM/IEEE conference on Supercomputing
An updated set of basic linear algebra subprograms (BLAS)
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Computational experiments with resultants for scaled Bernstein polynomials
Mathematical Methods for Curves and Surfaces
Stress calculations on multiply connected domains
Journal of Computational Physics
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Approximation of nonnegative functions by means of exponentiated trigonometric polynomials
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
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On the nature of the spectrum of the quasi-periodic Schrödinger operator
Nonlinear Analysis: Real World Applications
The Decompositional Approach to Matrix Computation
Computing in Science and Engineering
Recursive Array Layouts and Fast Matrix Multiplication
IEEE Transactions on Parallel and Distributed Systems
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Very large electronic structure calculations using an out-of-core filter-diagonalization method
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Real computations with fake numbers
Journal of Complexity
On the numerical evaluation of linear recurrences
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Rapid multiplication modulo the sum and difference of highly composite numbers
Mathematics of Computation
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Additive symmetries: the non-negative case
Theoretical Computer Science - Real numbers and computers
Rounding error analysis of two-stage iterative methods for large linear systems
Applied Mathematics and Computation
A comparison of parallel solvers for diagonally dominant and general narrow-banded linear systems
Parallel numerical linear algebra
Fault-Detection by Result-Checking for the Eigenproblem
EDCC-3 Proceedings of the Third European Dependable Computing Conference on Dependable Computing
Solving Orthogonal Matrix Differential Systems in Mathematica
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
Symplectic Methods for Separable Hamiltonian Systems
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
LAWRA: Linear Algebra with Recursive Algorithms
PARA '00 Proceedings of the 5th International Workshop on Applied Parallel Computing, New Paradigms for HPC in Industry and Academia
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PARA '00 Proceedings of the 5th International Workshop on Applied Parallel Computing, New Paradigms for HPC in Industry and Academia
PARA '02 Proceedings of the 6th International Conference on Applied Parallel Computing Advanced Scientific Computing
Real Computations with Fake Numbers
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
A Generic Library for Floating-Point Numbers and Its Application to Exact Computing
TPHOLs '01 Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics
Parallel Implementation of a Block Algorithm for Matrix 1-Norm Estimation
Euro-Par '01 Proceedings of the 7th International Euro-Par Conference Manchester on Parallel Processing
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Euro-Par '99 Proceedings of the 5th International Euro-Par Conference on Parallel Processing
Static Analyses of the Precision of Floating-Point Operations
SAS '01 Proceedings of the 8th International Symposium on Static Analysis
Fractal Matrix Multiplication: A Case Study on Portability of Cache Performance
WAE '01 Proceedings of the 5th International Workshop on Algorithm Engineering
Stability Analysis of Parallel Evaluation of Finite Series of Orthogonal Polynominals
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Stability of a Parallel Partitioning Algorithm for Special Classes of Banded Linear Systems
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Inversion of Symmetric Matrices in a New Block Packes Storage
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
An Algorithm Based on Orthogonal Polynominal Vectors for Toeplitz Least Squares Problems
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
An incremental method for computing dominant singular spaces
Computational information retrieval
Pseudozeros of multivariate polynomials
Mathematics of Computation
Numerical evaluation of the pth derivative of Jacobi series
Applied Numerical Mathematics
Highly accurate verified error bounds for Krylov type linear system solvers
Applied Numerical Mathematics
Computing tall skinny solutions of AX - XB = C
Mathematics and Computers in Simulation - MODELLING 2001 - Second IMACS conference on mathematical modelling and computational methods in mechanics, physics, biomechanics and geodynamics
Future Generation Computer Systems - Special issue: Geometric numerical algorithms
QR factorization with Morton-ordered quadtree matrices for memory re-use and parallelism
Proceedings of the ninth ACM SIGPLAN symposium on Principles and practice of parallel programming
The Program of Grand Challenge Problems: Expectations and Results
PAS '97 Proceedings of the 2nd AIZU International Symposium on Parallel Algorithms / Architecture Synthesis
Estimating differential quantities using polynomial fitting of osculating jets
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
J-lossless factorisations for robust H∞-control in delta-domain
Systems Analysis Modelling Simulation
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Informatics in education
Computer algebra handbook
Modified ST algorithms and numerical experiments
Applied Numerical Mathematics - Special issue: 2nd international workshop on numerical linear algebra, numerical methods for partial differential equations and optimization
Floating point arithmetic teaching for computational science
Future Generation Computer Systems - Special issue: Selected papers from the workshop on education in computational sciences held at the ICCS 2002
More accuracy at fixed precision
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
Computing the sign or the value of the determinant of an integer matrix, a complexity survey
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
A comparison of methods for accurate summation
ACM SIGSAM Bulletin
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Another preprocessing algorithm for generalized one-dimensional fast multipole method
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The aggregation and cancellation techniques as a practical tool for faster matrix multiplication
Theoretical Computer Science - Algebraic and numerical algorithm
Numerical factorization of multivariate complex polynomials
Theoretical Computer Science - Algebraic and numerical algorithm
High-performance linear algebra algorithms using new generalized data structures for matrices
IBM Journal of Research and Development
An error estimate for matrix equations
Applied Numerical Mathematics
Interval solutions for interval algebraic equations
Mathematics and Computers in Simulation - Special issue: Selected papers from the 4th IMACS symposium on mathematical modelling (4th MATHMOD)
On the computation of maximum minors of Hadamard matrices
Mathematics and Computers in Simulation - Special issue: Applications of computer algebra in science, engineering, simulation and special software
Analysis and applications of Priest's distillation
ACM Transactions on Mathematical Software (TOMS)
Optimizing aggregate array computations in loops
ACM Transactions on Programming Languages and Systems (TOPLAS)
Algorithm 841: BHESS: Gaussian reduction to a similar banded Hessenberg form
ACM Transactions on Mathematical Software (TOMS)
Estimating differential quantities using polynomial fitting of osculating jets
Computer Aided Geometric Design
Lidstone approximation on the triangle
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An overview of SuperLU: Algorithms, implementation, and user interface
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Specification and Management of QoS in Real-Time Databases Supporting Imprecise Computations
IEEE Transactions on Computers
Bridging ETAQA and Ramaswami's formula for the solution of M/G/1-type processes
Performance Evaluation - Performance 2005
Perturbing and evaluating numerical programs without recompilation: the wonglediff way
Software—Practice & Experience
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Pivoting for structured matrices and rational tangential interpolation
Contemporary mathematics
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Error bounds from extra-precise iterative refinement
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Semantics of roundoff error propagation in finite precision calculations
Higher-Order and Symbolic Computation
Solving linear programs with finite precision: II. algorithms
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Adaptive splitting for stabilizing 1-D wavelet decompositions on irregular grids
Signal Processing - Signal processing in UWB communications
Sensitivity Analysis: When a Little Means a Lot
Computing in Science and Engineering
Evaluation algorithms for multivariate polynomials in Bernstein--Bézier form
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Structured mixed and componentwise condition numbers of some structured matrices
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Growth factor and expected growth factor of some pivoting strategies
Journal of Computational and Applied Mathematics
A primal--dual symmetric relaxation for homogeneous conic systems
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An error analysis of the modified scaling and squaring method
Computers & Mathematics with Applications
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Efficient Solution of A, x(k) = b(k) Using A-1
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Minimum triangle separation for correct z-buffer occlusion
GH '06 Proceedings of the 21st ACM SIGGRAPH/EUROGRAPHICS symposium on Graphics hardware
Short communication: A note on cycling LP examples with permutation structure
Computers and Operations Research
Mixed Precision Iterative Refinement Techniques for the Solution of Dense Linear Systems
International Journal of High Performance Computing Applications
A structured rank-revealing method for Sylvester matrix
Journal of Computational and Applied Mathematics
Automatica (Journal of IFAC)
Algorithm 879: EIGENTEST—a test matrix generator for large-scale eigenproblems
ACM Transactions on Mathematical Software (TOMS)
On the Failure of Rank-Revealing QR Factorization Software -- A Case Study
ACM Transactions on Mathematical Software (TOMS)
Optimization Methods & Software
Validated Evaluation of Special Mathematical Functions
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
Narrowband Jammer Excision in CDMA Using Particle Swarm Optimization
ICIC '08 Proceedings of the 4th international conference on Intelligent Computing: Advanced Intelligent Computing Theories and Applications - with Aspects of Theoretical and Methodological Issues
GPCE '08 Proceedings of the 7th international conference on Generative programming and component engineering
Parameter optimization for differential equations in asset price forecasting
Optimization Methods & Software - Mathematical programming in data mining and machine learning
A numerical algorithm for zero counting, I: Complexity and accuracy
Journal of Complexity
Extra-Precise Iterative Refinement for Overdetermined Least Squares Problems
ACM Transactions on Mathematical Software (TOMS)
Iterative refinement for Neville elimination
International Journal of Computer Mathematics - RECENT ADVANCES IN COMPUTATIONAL AND APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING
Stability of block LU factorization for block tridiagonal matrices
Computers & Mathematics with Applications
Adaptive Winograd's matrix multiplications
ACM Transactions on Mathematical Software (TOMS)
The scaling and modified squaring method for matrix functions related to the exponential
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
Symbolic-numeric sparse interpolation of multivariate polynomials
Journal of Symbolic Computation
Lidstone approximation on the triangle
Applied Numerical Mathematics
Padé and Gregory error estimates for the logarithm of block triangular matrices
Applied Numerical Mathematics
Low cost high performance uncertainty quantification
Proceedings of the 2nd Workshop on High Performance Computational Finance
The loss of orthogonality in the Gram-Schmidt orthogonalization process
Computers & Mathematics with Applications
Bit precision analysis for compressed sensing
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
CCDC'09 Proceedings of the 21st annual international conference on Chinese control and decision conference
A note on level-2 condition numbers
Journal of Complexity
Solving linear programs with finite precision: II. Algorithms
Journal of Complexity
Journal of Computational and Applied Mathematics
Relaxation strategies for nested Krylov methods
Journal of Computational and Applied Mathematics
On the degree elevation of Bernstein polynomial representation
Journal of Computational and Applied Mathematics
Rectangular full packed format for cholesky's algorithm: factorization, solution, and inversion
ACM Transactions on Mathematical Software (TOMS)
Journal of Computational and Applied Mathematics
V-invariant methods for generalised least squares problems
ICCS'03 Proceedings of the 2003 international conference on Computational science: PartIII
Exact real computation in computer algebra
SNSC'01 Proceedings of the 2nd international conference on Symbolic and numerical scientific computation
A determinantal approach to Appell polynomials
Journal of Computational and Applied Mathematics
LU factoring of non-invertible matrices
ACM Communications in Computer Algebra
Energy efficient hardware architecture of LU triangularization for MIMO receiver
IEEE Transactions on Circuits and Systems II: Express Briefs
Performance analysis of Cooley-Tukey FFT algorithms for a many-core architecture
SpringSim '10 Proceedings of the 2010 Spring Simulation Multiconference
Using hybrid CPU-GPU platforms to accelerate the computation of the matrix sign function
Euro-Par'09 Proceedings of the 2009 international conference on Parallel processing
PPAM'09 Proceedings of the 8th international conference on Parallel processing and applied mathematics: Part II
Stabilization and optimization of PLUS factorization and its application in image coding
Journal of Visual Communication and Image Representation
Weber-Fechner Law and the Optimality of the Logarithmic Scale
Minds and Machines
An error correction solver for linear systems: evaluation of mixed precision implementations
VECPAR'10 Proceedings of the 9th international conference on High performance computing for computational science
A note on shifted Hessenberg systems and frequency response computation
ACM Transactions on Mathematical Software (TOMS)
Sampling algebraic sets in local intrinsic coordinates
Computers & Mathematics with Applications
Bernstein Bezoutians and application to intersection problems
Computer Aided Geometric Design
Stability of the Levinson Algorithm for Toeplitz-Like Systems
SIAM Journal on Matrix Analysis and Applications
Smoothed Analysis of Moore-Penrose Inversion
SIAM Journal on Matrix Analysis and Applications
Applying Metric Regularity to Compute a Condition Measure of a Smoothing Algorithm for Matrix Games
SIAM Journal on Optimization
Rigorous Enclosures of Ellipsoids and Directed Cholesky Factorizations
SIAM Journal on Matrix Analysis and Applications
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Fast algorithms for floating-point interval matrix multiplication
Journal of Computational and Applied Mathematics
A condensation-based application of Cramer's rule for solving large-scale linear systems
Journal of Discrete Algorithms
Parallelising matrix operations on clusters for an optimal control-based quantum compiler
Euro-Par'06 Proceedings of the 12th international conference on Parallel Processing
VECPAR'04 Proceedings of the 6th international conference on High Performance Computing for Computational Science
Stability of block LU factorization for block tridiagonal block H-matrices
Journal of Computational and Applied Mathematics
A note on matrices with maximal growth factor for Neville elimination
Journal of Computational and Applied Mathematics
Alan turing: the logical and physical basis of computing
Turing'04 Proceedings of the 2004 international conference on Alan Mathison Turing: a celebration of his life and achievements
Low-cost data uncertainty quantification
Concurrency and Computation: Practice & Experience
Performance of perturbation methods on orbit prediction
Mathematical and Computer Modelling: An International Journal
Smooth and adaptive gradient method with retards
Mathematical and Computer Modelling: An International Journal
An overview on the eigenvalue computation for matrices
Neural, Parallel & Scientific Computations
Exploiting eye-hand coordination to detect grasping movements
Image and Vision Computing
Original article: Further properties of random orthogonal matrix simulation
Mathematics and Computers in Simulation
A framework for evaluating the smoothness of data-mining results
ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part II
Iterative refinement techniques for solving block linear systems of equations
Applied Numerical Mathematics
Δh-Appell sequences and related interpolation problem
Numerical Algorithms
Computer Methods and Programs in Biomedicine
High-Precision Numerical Simulations on a CUDA GPU: Kerr Black Hole Tails
Journal of Scientific Computing
Minimizing synchronizations in sparse iterative solvers for distributed supercomputers
Computers & Mathematics with Applications
Computation of the monodromy matrix in floating point arithmetic with the Wilkinson Model
Computers & Mathematics with Applications
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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.