Algebraic theory of fast mixed-radix transforms. II. Computational complexity and applications
Displaying 21 – 40 of 97
Algorithms in Unnormalized Arithmetic. II. Unrestricted Polynomial Evaluation.
N. METROPOLIS, M. MENZEL (1967)
Numerische Mathematik
An adaptive -step conjugate gradient algorithm with dynamic basis updating
Erin Claire Carson (2020)
Applications of Mathematics
The adaptive -step CG algorithm is a solver for sparse symmetric positive definite linear systems designed to reduce the synchronization cost per iteration while still achieving a user-specified accuracy requirement. In this work, we improve the adaptive -step conjugate gradient algorithm by the use of iteratively updated estimates of the largest and smallest Ritz values, which give approximations of the largest and smallest eigenvalues of , using a technique due to G. Meurant and P. Tichý (2018)....
An alternating direction implicit method for orthogonal spline collocation linear systems.
Bernard Bialecki (1991)
Numerische Mathematik
An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations
Éric Boillat (2001)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
In this article, we consider the initial value problem which is obtained after a space discretization (with space step ) of the equations governing the solidification process of a multicomponent alloy. We propose a numerical scheme to solve numerically this initial value problem. We prove an error estimate which is not affected by the step size chosen in the space discretization. Consequently, our scheme provides global convergence without any stability condition between and the time step size...
An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations
Éric Boillat (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
In this article, we consider the initial value problem which is obtained after a space discretization (with space step h) of the equations governing the solidification process of a multicomponent alloy. We propose a numerical scheme to solve numerically this initial value problem. We prove an error estimate which is not affected by the step size h chosen in the space discretization. Consequently, our scheme provides global convergence without any stability condition between h and the time...
An introduction to hierarchical matrices
Hackbusch, Wolfgang, Grasedyck, Lars, Börm, Steffen (2002)
Proceedings of Equadiff 10
An introduction to hierarchical matrices
Wolfgang Hackbusch, Lars Grasedyck, Steffen Börm (2002)
Mathematica Bohemica
We give a short introduction to a method for the data-sparse approximation of matrices resulting from the discretisation of non-local operators occurring in boundary integral methods or as the inverses of partial differential operators. The result of the approximation will be the so-called hierarchical matrices (or short -matrices). These matrices form a subset of the set of all matrices and have a data-sparse representation. The essential operations for these matrices (matrix-vector and matrix-matrix...
Application of a Higher Order Discontinuous Galerkin
A. V. Wolkov, Ch. Hirsch, N. B. Petrovskaya (2011)
Mathematical Modelling of Natural Phenomena
We discuss the issues of implementation of a higher order discontinuous Galerkin (DG) scheme for aerodynamics computations. In recent years a DG method has intensively been studied at Central Aerohydrodynamic Institute (TsAGI) where a computational code has been designed for numerical solution of the 3-D Euler and Navier-Stokes equations. Our discussion is mainly based on the results of the DG study conducted in TsAGI in collaboration with the NUMECA...
Approximation of invariant surfaces by periodic orbits in high-dimensional maps: Some rigorous results.
Tompaidis, Stathis (1996)
Experimental Mathematics
Automatic differentiation platform : design
Christèle Faure (2002)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Automatic differentiation (AD) has proven its interest in many fields of applied mathematics, but it is still not widely used. Furthermore, existing numerical methods have been developed under the hypotheses that computing program derivatives is not affordable for real size problems. Exact derivatives have therefore been avoided, or replaced by approximations computed by divided differences. The hypotheses is no longer true due to the maturity of AD added to the quick evolution of machine capacity....
Automatic Differentiation Platform: Design
Christèle Faure (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
Automatic differentiation (AD) has proven its interest in many fields of applied mathematics, but it is still not widely used. Furthermore, existing numerical methods have been developed under the hypotheses that computing program derivatives is not affordable for real size problems. Exact derivatives have therefore been avoided, or replaced by approximations computed by divided differences. The hypotheses is no longer true due to the maturity of AD added to the quick evolution of machine capacity....
Berkowitz's algorithm and clow sequences.
Soltys, Michael (2002)
ELA. The Electronic Journal of Linear Algebra [electronic only]
Breaking the curse of dimensionality [Book]
Markus Weimar (2015)
Bubble-enriched least-squares finite element method for transient advective transport.
Kumar, Rajeev, Dennis, Brian H. (2008)
Differential Equations & Nonlinear Mechanics
Cache optimization for structured and unstructured grid multigrid.
Douglas, Craig C., Hu, Jonathan, Kowarschik, Markus, Rüde, Ulrich, Weiss, Christian (2000)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
Checking nonsingularity of tridiagonal matrices.
Bar-On, Ilan (1999)
ELA. The Electronic Journal of Linear Algebra [electronic only]
Checking positive definiteness or stability of symmetric interval matrices is NP-hard
Jiří Rohn (1994)
Commentationes Mathematicae Universitatis Carolinae
It is proved that checking positive definiteness, stability or nonsingularity of all [symmetric] matrices contained in a symmetric interval matrix is NP-hard.
Coarsening invariance and bucket-sorted independent sets for algebraic multigrid.
Alber, David M., Olson, Luke N. (2010)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
Complexity issues for the symmetric interval eigenvalue problem
Milan Hladík (2015)
Open Mathematics
We study the problem of computing the maximal and minimal possible eigenvalues of a symmetric matrix when the matrix entries vary within compact intervals. In particular, we focus on computational complexity of determining these extremal eigenvalues with some approximation error. Besides the classical absolute and relative approximation errors, which turn out not to be suitable for this problem, we adapt a less known one related to the relative error, and also propose a novel approximation error....