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Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 05/2019, Volume 88, Issue 317, pp. 1189 - 1228
Journal Article
BIT Numerical Mathematics, ISSN 0006-3835, 12/2015, Volume 55, Issue 4, pp. 1057 - 1103
We consider numerical approximations of stochastic Langevin equations by implicit methods. We show a weak backward error analysis result in the sense that the... 
Weak error | Computational Mathematics and Numerical Analysis | 37M25 | Numeric Computing | Backward error analysis | Mathematics | Exponential mixing | Numerical scheme | 65C30 | Langevin equation | Mathematics, general | Kolmogorov equation | 60H35 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | MODIFIED EQUATIONS | Probability | Numerical Analysis
Journal Article
SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2012, Volume 50, Issue 3, pp. 1735 - 1752
Journal Article
BIT Numerical Mathematics, ISSN 0006-3835, 9/2019, Volume 59, Issue 3, pp. 613 - 646
Journal Article
SIAM Journal on Scientific Computing, ISSN 1064-8275, 2016, Volume 38, Issue 3, pp. A1639 - A1661
The Leja method is a polynomial interpolation procedure that can be used to compute matrix functions. In particular, computing the action of the matrix... 
Leja interpolation | Backward error analysis | Taylor series | Action of matrix exponential | φ functions | Exponential integrators | INTERPOLATION | MATHEMATICS, APPLIED | exponential integrators | phi functions | backward error analysis | action of matrix exponential | Mathematics - Numerical Analysis
Journal Article
BIT Numerical Mathematics, ISSN 0006-3835, 03/2019, Volume 59, Issue 1, pp. 271 - 297
When polynomial roots vary widely in order of magnitude, severe numerical instability problem may occur due to deflation schemes. Peters and Wilkinson (IMA J... 
Backward error analysis | Polynomial deflation | Tropical polynomial | EIGENVALUE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | Deflation (Finance) | Analysis
Journal Article
Mathematical Programming, ISSN 0025-5610, 2019, Volume 180, Issue 1-2, pp. 371 - 416
This paper reveals that a common and central role, played in many error bound (EB) conditions and a variety of gradient-type methods, is a residual measure... 
Dual objective function | Gradient descent | Residual measure operator | Linear convergence | Proximal alternating linearized minimization | Error bound | Forward–backward splitting algorithm | Nesterov’s acceleration | Proximal point algorithm | Algorithms | Ascent | Measurement methods | Convexity | Optimization | Linearization | Convergence
Journal Article
SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, 2016, Volume 37, Issue 1, pp. 123 - 144
We perform a backward error analysis of polynomial eigenvalue problems solved via linearization. Through the use of dual minimal bases, we unify the... 
Backward error | Stability | Dual minimal basis | Polynomial eigenvalue problem | Linearization | Strong linearization | MATRIX | MATHEMATICS, APPLIED | strong linearization | backward error | dual minimal basis | polynomial eigenvalue problem | EIGENPROBLEMS | stability | linearization
Journal Article
by Qi, RS and Wang, XJ
JOURNAL OF SCIENTIFIC COMPUTING, ISSN 0885-7474, 08/2019, Volume 80, Issue 2, pp. 1171 - 1194
Strong approximation errors of both finite element semi-discretization and spatio-temporal full discretization are analyzed for the stochastic Allen-Cahn... 
Additive noise | Strong approximation | Finite element method | MATHEMATICS, APPLIED | Stochastic Allen-Cahn equation | DISCRETIZATION | APPROXIMATION | DIFFERENTIAL-EQUATIONS | TIME | Backward Euler scheme | STRONG-CONVERGENCE | Analysis | Methods
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 07/2018, Volume 76, Issue 2, pp. 340 - 360
We present an a posteriori error analysis of the fully discretized time-dependent Darcy and Stokes equations, that models laminar fluid flow over a porous... 
A posteriori error analysis | Finite elements | Darcy equations | Backward Euler scheme | Stokes equations | POROUS-MEDIA FLOW | MATHEMATICS, APPLIED | PARABOLIC EQUATIONS | FLUID-FLOW | MODEL | FINITE-ELEMENT-METHOD
Journal Article
IMA Journal of Numerical Analysis, ISSN 0272-4979, 03/2015, Volume 35, Issue 2, pp. 583 - 614
Journal Article
Applied Numerical Mathematics, ISSN 0168-9274, 02/2019, Volume 136, pp. 23 - 45
This paper is concerned with residual type a posteriori error estimates of fully discrete finite element approximations for parabolic optimal control problems... 
A posteriori error estimates | Measure data in time | Parabolic optimal control problem | Measure data in space | The backward Euler scheme | Finite element approximations | MATHEMATICS, APPLIED | PRIORI | EQUATIONS
Journal Article
Numerical Linear Algebra with Applications, ISSN 1070-5325, 08/2019, Volume 26, Issue 4, p. n/a
Summary Heavily damped quadratic eigenvalue problem (QEP) is a special type of QEPs. It has a large gap between small and large eigenvalues in absolute value.... 
growth factor | heavily damped QEP | linearizations | backward error | MATHEMATICS | MATHEMATICS, APPLIED | PERTURBATION | ALGORITHM | Eigenvalues | Error analysis | Upper bounds | Growth factors | Eigen values
Journal Article
Inverse Problems, ISSN 0266-5611, 03/2017, Volume 33, Issue 4, p. 44001
Journal Article
International Journal of Computer Mathematics: A special collection of papers relating to computational linear algebra and nonlinear equation solvers, ISSN 0020-7160, 08/2019, Volume 96, Issue 8, pp. 1603 - 1622
Journal Article
Econometrica, ISSN 0012-9682, 5/2017, Volume 85, Issue 3, pp. 991 - 1012
Journal Article
BIT Numerical Mathematics, ISSN 0006-3835, 12/2018, Volume 58, Issue 4, pp. 907 - 935
Journal Article
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