A rational deferred correction approach to parabolic optimal control problems

The accurate and efficient solution of time-dependent PDE-constrained optimization problems is a challenging task, in large part due to the very high dimension of the matrix systems that need to be solved. We devise a new deferred correction method for coupled systems of time-dependent PDEs, allowing one to iteratively improve the accuracy of low-order time stepping schemes. We consider two variants of our method, a splitting and a coupling version, and analyze their convergence properties. We then test our approach on a number of PDE-constrained optimization problems. We obtain solution accuracies far superior to that achieved when solving a single discretized problem, in particular in cases where the accuracy is limited by the time discretization. Our approach allows for the direct reuse of existing solvers for the resulting matrix systems, as well as state-of-the-art preconditioning strategies

Near-optimal perfectly matched layers for indefinite Helmholtz problems

A new construction of an absorbing boundary condition for indefinite Helmholtz problems on unbounded domains is presented. This construction is based on a near-best uniform rational interpolant of the inverse square root function on the union of a negative and positive real interval, designed with the help of a classical result by Zolotarev. Using Krein's interpretation of a Stieltjes continued fraction, this interpolant can be converted into a three-term finite difference discretization of a perfectly matched layer (PML) which converges exponentially fast in the number of grid points. The convergence rate is asymptotically optimal for both propagative and evanescent wave modes. Several numerical experiments and illustrations are included.Comment: Accepted for publication in SIAM Review. To appear 201

Krylov Subspace Recycling With Randomized Sketching For Matrix Functions

A Krylov subspace recycling method for the efficient evaluation of a sequence of matrix functions acting on a set of vectors is developed. The method improves over the recycling methods presented in [Burke et al., arXiv:2209.14163, 2022] in that it uses a closed-form expression for the augmented FOM approximants and hence circumvents the use of numerical quadrature. We further extend our method to use randomized sketching in order to avoid the arithmetic cost of orthogonalizing a full Krylov basis, offering an attractive solution to the fact that recycling algorithms built from shifted augmented FOM cannot easily be restarted. The efficacy of the proposed algorithms is demonstrated with numerical experiments.Comment: 19 pages, 5 figure

A sketch-and-select Arnoldi process

A sketch-and-select Arnoldi process to generate a well-conditioned basis of a Krylov space is proposed. At each iteration the procedure utilizes randomized sketching to select a limited number of previously computed basis vectors to project out of the current basis vector. The computational cost grows linearly with the dimension of the Krylov basis. The subset selection problem for the projection step is approximately solved with a number of heuristic algorithms and greedy methods used in statistical learning and compressive sensing

Randomized sketching of nonlinear eigenvalue problems

Rational approximation is a powerful tool to obtain accurate surrogates for nonlinear functions that are easy to evaluate and linearize. The interpolatory adaptive Antoulas--Anderson (AAA) method is one approach to construct such approximants numerically. For large-scale vector- and matrix-valued functions, however, the direct application of the set-valued variant of AAA becomes inefficient. We propose and analyze a new sketching approach for such functions called sketchAAA that, with high probability, leads to much better approximants than previously suggested approaches while retaining efficiency. The sketching approach works in a black-box fashion where only evaluations of the nonlinear function at sampling points are needed. Numerical tests with nonlinear eigenvalue problems illustrate the efficacy of our approach, with speedups above 200 for sampling large-scale black-box functions without sacrificing on accuracy.Comment: 15 page

Different Ambidextrous Learning Architectures and the Role of HRM Systems

During the past decade ambidexterity has emerged as the central research stream in organization science to investigate how organizations manage to remain successful over time. By using the lens of organizational learning, ambidexterity can be defined as the simultaneous pursuit of exploration and exploitation. However, the link between ambidexterity and the human resource management of a firm is still a blind spot on the ambidexterity research map. To shed light on this issue, we show how different ambidextrous learning architectures can be created and maintained by the means of consistent HRM systems. By doing so, we show how HRM systems as specific bundles of HRM practices facilitate ambidextrous learning. Thereby we emphasize the challenge of creating and sustaining the horizontal and vertical fit of an HRM system with regard to different ambidextrous designs.Ambidexterity; Exploration; Exploitation; Organizational Learning; HRM; Strategic Human Resource Management

ABBA: adaptive Brownian bridge-based symbolic aggregation of time series

From Springer Nature via Jisc Publications RouterHistory: received 2019-05-29, accepted 2020-05-14, registration 2020-05-14, pub-electronic 2020-06-03, online 2020-06-03, pub-print 2020-07Publication status: PublishedFunder: Engineering and Physical Sciences Research Council; doi: http://dx.doi.org/10.13039/50110000026; Grant(s): EP/N509565/1Abstract: A new symbolic representation of time series, called ABBA, is introduced. It is based on an adaptive polygonal chain approximation of the time series into a sequence of tuples, followed by a mean-based clustering to obtain the symbolic representation. We show that the reconstruction error of this representation can be modelled as a random walk with pinned start and end points, a so-called Brownian bridge. This insight allows us to make ABBA essentially parameter-free, except for the approximation tolerance which must be chosen. Extensive comparisons with the SAX and 1d-SAX representations are included in the form of performance profiles, showing that ABBA is often able to better preserve the essential shape information of time series compared to other approaches, in particular when time warping measures are used. Advantages and applications of ABBA are discussed, including its in-built differencing property and use for anomaly detection, and Python implementations provided

Sheep in Wolf’s Clothing: The Role of Artifacts in Interpretive Schema Change

In this paper, we investigate the role of artifacts in a failed project that aimed at implementing a new culture of dealing with errors in a hospital by transferring safety standards from the aviation industry. We apply the interpretative method of objective hermeneutics to elucidate the role of artifacts as linking pins between diverging interpretive schemata and collective action during attempts to modify organizational routines. In particular, we show how the implementation of artifacts may serve as a means to satisfy a new espoused schema, while at the same time they are created and interpreted in ways that strengthen the old enacted schema. Although on the surface everyone would appreciate changes in treatment routines that help to avoid errors, the guiding norms of individual vigilance and self-centeredness, a culture that emphasizes hierarchy as a core value as well as the lack of sanctions for enacting the old schema led to a situation where the new espoused schema was never enacted. Instead, artifacts were used to stabilize a divergence between espoused and enacted schemata. Failure remained a cultural taboo.(VLID)342667