Improving the compensated Horner scheme with a fused multiply and add
Proceedings of the 2006 ACM symposium on Applied computing
Super-fast validated solution of linear systems
Journal of Computational and Applied Mathematics - Special issue: Scientific computing, computer arithmetic, and validated numerics (SCAN 2004)
A method of obtaining verified solutions for linear systems suited for Java
Journal of Computational and Applied Mathematics - Special issue: Scientific computing, computer arithmetic, and validated numerics (SCAN 2004)
Convergence of Rump's method for inverting arbitrarily ill-conditioned matrices
Journal of Computational and Applied Mathematics
The schur aggregation for solving linear systems of equations
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Studies of the discontinuous enrichment method for two-dimensional acoustics
Finite Elements in Analysis and Design
Additive preconditioning and aggregation in matrix computations
Computers & Mathematics with Applications
A parallel algorithm for accurate dot product
Parallel Computing
Accurate simple zeros of polynomials in floating point arithmetic
Computers & Mathematics with Applications
Schur aggregation for linear systems and determinants
Theoretical Computer Science
A new error-free floating-point summation algorithm
Computers & Mathematics with Applications
High Performance Computing for Computational Science - VECPAR 2008
Dense linear system: a parallel self-verified solver
International Journal of Parallel Programming
A Modified Staggered Correction Arithmetic with Enhanced Accuracy and Very Wide Exponent Range
Numerical Validation in Current Hardware Architectures
Numerical Validation in Current Hardware Architectures
Error-Free Transformation in Rounding Mode toward Zero
Numerical Validation in Current Hardware Architectures
Fast (Parallel) Dense Linear System Solvers in C-XSC Using Error Free Transformations and BLAS
Numerical Validation in Current Hardware Architectures
A Note on Solving Problem 7 of the SIAM 100-Digit Challenge Using C-XSC
Numerical Validation in Current Hardware Architectures
Proceedings of the 2009 conference on Symbolic numeric computation
Computing correctly rounded integer powers in floating-point arithmetic
ACM Transactions on Mathematical Software (TOMS)
Optimizing a parallel self-verified method for solving linear systems
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
Algorithm 908: Online Exact Summation of Floating-Point Streams
ACM Transactions on Mathematical Software (TOMS)
Accurate evaluation of a polynomial and its derivative in Bernstein form
Computers & Mathematics with Applications
Accuracy versus time: a case study with summation algorithms
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
Verified Computation of Square Roots of a Matrix
SIAM Journal on Matrix Analysis and Applications
Accurate floating point arithmetic through hardware error-free transformations
ARC'11 Proceedings of the 7th international conference on Reconfigurable computing: architectures, tools and applications
Proofs of numerical programs when the compiler optimizes
Innovations in Systems and Software Engineering
Accurate Matrix Factorization: Inverse LU and Inverse QR Factorizations
SIAM Journal on Matrix Analysis and Applications
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
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
Comments on fast and exact accumulation of products
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume 2
Using C-XSC for high performance verified computing
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume 2
Cache-Oblivious algorithms and matrix formats for computations on interval matrices
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume 2
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
Accurate evaluation algorithm for bivariate polynomial in Bernstein-Bézier form
Applied Numerical Mathematics
Verified Bounds for Least Squares Problems and Underdetermined Linear Systems
SIAM Journal on Matrix Analysis and Applications
Accurate solution of dense linear systems, part I: Algorithms in rounding to nearest
Journal of Computational and Applied Mathematics
A new abstract domain for the representation of mathematically equivalent expressions
SAS'12 Proceedings of the 19th international conference on Static Analysis
Accurate evaluation of the k-th derivative of a polynomial and its application
Journal of Computational and Applied Mathematics
Accurate computing elementary symmetric functions
ACM Communications in Computer Algebra
ACM Transactions on Mathematical Software (TOMS)
Minimizing synchronizations in sparse iterative solvers for distributed supercomputers
Computers & Mathematics with Applications
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We discuss a multigrid approach to the optimization of systems governed by differential equations. Such optimization problems appear in many applications and are of a different nature than systems of equations. Our approach uses an optimization-based ...