Augmented Implicitly Restarted Lanczos Bidiagonalization Methods

Baglama, James; Reichel, Lothar

doi:10.1137/04060593x

Cited by 299 publications

(326 citation statements)

References 26 publications

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“…This approach proved advantageous in terms of the time needed for the truncation. Alternative ways to compute the truncated SVD are possible and can be found in [16,3,24]. The cost of computing the truncation depends, for example in the truncated SVD approach, on the cost of multiplying with the matrix UV T .…”

Section: Truncation Operator and Matrix Inner Productsmentioning

confidence: 99%

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Low-Rank Solution of Unsteady Diffusion Equations with Stochastic Coefficients

Benner

Onwunta

Stoll

2015

SIAM/ASA J. Uncertainty Quantification

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Abstract. We study the solution of linear systems resulting from the discretization of unsteady diffusion equations with stochastic coefficients. In particular, we focus on those linear systems that are obtained using the so-called stochastic Galerkin finite element method (SGFEM). These linear systems are usually very large with Kronecker product structure, and thus solving them can be both time-and computer memory-consuming. Under certain assumptions, we show that the solution of such linear systems can be approximated with a vector of low tensor rank. We then solve the linear systems using low-rank preconditioned iterative solvers. Numerical experiments demonstrate that these lowrank preconditioned solvers are effective, especially when the fluctuations in the random data are not too large relative to their mean values.

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Section: Truncation Operator and Matrix Inner Productsmentioning

confidence: 99%

“…Additionally, we have to ensure that the inner products within the iterative solver are computed efficiently. Due to the properties of the trace operator, 3 we are in luck, as…”

Section: Truncation Operator and Matrix Inner Productsmentioning

confidence: 99%

Low-Rank Solution of Unsteady Diffusion Equations with Stochastic Coefficients

Benner

Onwunta

Stoll

2015

SIAM/ASA J. Uncertainty Quantification

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“…In our analysis we used the "irlba" toolbox [4] in R and its implementation of the SVD algorithm [27] to produce a more compact dataset. The SVD method transforms the matrix P as:…”

Section: High Dimensionality and Sparsity Challengementioning

confidence: 99%

Reconciling mobile app privacy and usability on smartphones

Liu

Lin

Sadeh

2014

Proceedings of the 23rd International Conference on World Wide Web

121

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As they compete for developers, mobile app ecosystems have been exposing a growing number of APIs through their software development kits. Many of these APIs involve accessing sensitive functionality and/or user data and require approval by users. Android for instance allows developers to select from over 130 possible permissions. Expecting users to review and possibly adjust settings related to these permissions has proven unrealistic.In this paper, we report on the results of a study analyzing people's privacy preferences when it comes to granting permissions to different mobile apps. Our results suggest that, while people's mobile app privacy preferences are diverse, a relatively small number of profiles can be identified that offer the promise of significantly simplifying the decisions mobile users have to make. Specifically, our results are based on the analysis of settings of 4.8 million smartphone users of a mobile security and privacy platform. The platform relies on a rooted version of Android where users are allowed to choose between "granting", "denying" or "requesting to be dynamically prompted" when it comes to granting 12 different Android permissions to mobile apps they have downloaded.

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“…For inventor citations use a binary patent by inventor matrix with the positive cells representing a citation relationship between a patent and an inventor. Given the size of the matrices (millions by tens of thousands), a SVD approximation algorithm may be preferred, such as Lanczos (Baglama et al 2005). …”

Section: Machine Learning Methodsologiesmentioning

confidence: 99%

Automated patent landscaping

Abood

Feltenberger

2018

Artif Intell Law

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Patent landscaping is the process of finding patents related to a particular topic. It is important for companies, investors, governments, and academics seeking to gauge innovation and assess risk. However, there is no broadly recognized best approach to landscaping. Frequently, patent landscaping is a bespoke human-driven process that relies heavily on complex queries over bibliographic patent databases. In this paper, we present Automated Patent Landscaping, an approach that jointly leverages human domain expertise, heuristics based on patent metadata, and machine learning to generate high-quality patent landscapes with minimal effort. In particular, this paper describes a flexible automated methodology to construct a patent landscape for a topic based on an initial seed set of patents. This approach takes human-selected seed patents that are representative of a topic, such as operating systems, and uses structure inherent in patent data such as references and class codes to ''expand'' the seed set to a set of ''probably-related'' patents and anti-seed ''probably-unrelated'' patents. The expanded set of patents is then pruned with a semi-supervised machine learning model trained on seed and anti-seed patents. This removes patents from the expanded set that are unrelated to the topic and ensures a comprehensive and accurate landscape.

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Augmented Implicitly Restarted Lanczos Bidiagonalization Methods

Cited by 299 publications

References 26 publications

Low-Rank Solution of Unsteady Diffusion Equations with Stochastic Coefficients

Low-Rank Solution of Unsteady Diffusion Equations with Stochastic Coefficients

Reconciling mobile app privacy and usability on smartphones

Automated patent landscaping

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