Related papers: Error formulas for block rational Krylov approxima…
We introduce an algorithm for estimating the trace of a matrix function $f(\mathbf{A})$ using implicit products with a symmetric matrix $\mathbf{A}$. Existing methods for implicit trace estimation of a matrix function tend to treat…
In this paper we continue the investigation of partition functions of critical systems on a rectangle initiated in [R. Bondesan et al, Nucl.Phys.B862:553-575,2012]. Here we develop a general formalism of rectangle boundary states using…
The quadratic numerical range $W^2(A)$ is a subset of the standard numerical range of a linear operator which still contains its spectrum. It arises naturally in operators which have a $2 \times 2$ block structure, and it consists of at…
Floating point error is a drawback of embedded systems implementation that is difficult to avoid. Computing rigorous upper bounds of roundoff errors is absolutely necessary for the validation of critical software. This problem of computing…
The numerical computation of equilibrium reward gradients for Markov chains appears in many applications for example within the policy improvement step arising in connection with average reward stochastic dynamic programming. When the state…
Splitting methods constitute a widely used class of numerical integrators for ordinary and partial differential equations, particularly well suited to problems that can be decomposed into simpler subproblems. High-order splitting schemes…
We formulate a set of general rules for computing $d$-dimensional four-point global conformal blocks of operators in arbitrary Lorentz representations in the context of the embedding space operator product expansion formalism…
In this research, we solve polynomial, Sobolev polynomial, rational, and Sobolev rational least squares problems. Although the increase in the approximation degree allows us to fit the data better in attacking least squares problems, the…
Matrix functions are a central topic of linear algebra, and problems requiring their numerical approximation appear increasingly often in scientific computing. We review various limited-memory methods for the approximation of the action of…
A well-known problem in computing some matrix functions iteratively is the lack of a clear, commonly accepted residual notion. An important matrix function for which this is the case is the matrix exponential. Suppose the matrix exponential…
We study the kinematics of correlation functions of local and extended operators in a conformal field theory. We present a new method for constructing the tensor structures associated to primary operators in an arbitrary bosonic…
We prove sharp, computable error estimates for the propagation of errors in the numerical solution of ordinary differential equations. The new estimates extend previous estimates of the influence of data errors and discretisation errors…
Modern lunar-planetary ephemerides are numerically integrated on the observational timespan of more than 100 years (with the last 20 years having very precise astrometrical data). On such long timespans, not only finite difference…
We derive a priori residual-type bounds for the Arnoldi approximation of a matrix function and a strategy for setting the iteration accuracies in the inexact Arnoldi approximation of matrix functions. Such results are based on the decay…
We investigate the rational approximation of fractional powers of unbounded positive operators attainable with a specific integral representation of the operator function. We provide accurate error bounds by exploiting classical results in…
Motivated by recommendation systems, we consider the problem of estimating block constant binary matrices (of size $m \times n$) from sparse and noisy observations. The observations are obtained from the underlying block constant matrix…
We develop a group theoretical formalism to study correlation functions in defect conformal field theory, with multiple insertions of bulk and defect fields. This formalism is applied to construct the defect conformal blocks for three-point…
In this paper, we develop algorithms for computing the recurrence coefficients corresponding to multiple orthogonal polynomials on the step-line. We reformulate the problem as an inverse eigenvalue problem, which can be solved using…
Krylov methods rely on iterated matrix-vector products $A^k u_j$ for an $n\times n$ matrix $A$ and vectors $u_1,\ldots,u_m$. The space spanned by all iterates $A^k u_j$ admits a particular basis -- the \emph{maximal Krylov basis} -- which…
A class of linear parabolic equations is considered. We derive a framework for the a posteriori error analysis of time discretisations by Richardson extrapolation of arbitrary order combined with finite element discretisations in space. We…