MINRES-QLP: a Krylov subspace method for indefinite or singular symmetric systems

CG, SYMMLQ, and MINRES are Krylov subspace methods for solving symmetric systems of linear equations. When these methods are applied to an incompatible system (that is, a singular symmetric least-squares problem), CG could break down and SYMMLQ's solution could explode, while MINRES would give a least-squares solution but not necessarily the minimum-length (pseudoinverse) solution. This understanding motivates us to design a MINRES-like algorithm to compute minimum-length solutions to singular symmetric systems. MINRES uses QR factors of the tridiagonal matrix from the Lanczos process (where R is upper-tridiagonal). MINRES-QLP uses a QLP decomposition (where rotations on the right reduce R to lower-tridiagonal form). On ill-conditioned systems (singular or not), MINRES-QLP can give more accurate solutions than MINRES. We derive preconditioned MINRES-QLP, new stopping rules, and better estimates of the solution and residual norms, the matrix norm, and the condition number.Comment: 26 pages, 6 figure

Challenges in Developing Great Quasi-Monte Carlo Software

Quasi-Monte Carlo (QMC) methods have developed over several decades. With the explosion in computational science, there is a need for great software that implements QMC algorithms. We summarize the QMC software that has been developed to date, propose some criteria for developing great QMC software, and suggest some steps toward achieving great software. We illustrate these criteria and steps with the Quasi-Monte Carlo Python library (QMCPy), an open-source community software framework, extensible by design with common programming interfaces to an increasing number of existing or emerging QMC libraries developed by the greater community of QMC researchers

Summary of the First Workshop on Sustainable Software for Science: Practice and Experiences (WSSSPE1)

Challenges related to development, deployment, and maintenance of reusable software for science are becoming a growing concern. Many scientists’ research increasingly depends on the quality and availability of software upon which their works are built. To highlight some of these issues and share experiences, the First Workshop on Sustainable Software for Science: Practice and Experiences (WSSSPE1) was held in November 2013 in conjunction with the SC13 Conference. The workshop featured keynote presentations and a large number (54) of solicited extended abstracts that were grouped into three themes and presented via panels. A set of collaborative notes of the presentations and discussion was taken during the workshop. Unique perspectives were captured about issues such as comprehensive documentation, development and deployment practices, software licenses and career paths for developers. Attribution systems that account for evidence of software contribution and impact were also discussed. These include mechanisms such as Digital Object Identifiers, publication of “software papers”, and the use of online systems, for example source code repositories like GitHub. This paper summarizes the issues and shared experiences that were discussed, including cross-cutting issues and use cases. It joins a nascent literature seeking to understand what drives software work in science, and how it is impacted by the reward systems of science. These incentives can determine the extent to which developers are motivated to build software for the long-term, for the use of others, and whether to work collaboratively or separately. It also explores community building, leadership, and dynamics in relation to successful scientific software

Report on the Third Workshop on Sustainable Software for Science: Practice and Experiences (WSSSPE3)

This report records and discusses the Third Workshop on Sustainable Software for Science: Practice and Experiences (WSSSPE3). The report includes a description of the keynote presentation of the workshop, which served as an overview of sustainable scientific software. It also summarizes a set of lightning talks in which speakers highlighted to-the-point lessons and challenges pertaining to sustaining scientific software. The final and main contribution of the report is a summary of the discussions, future steps, and future organization for a set of self-organized working groups on topics including developing pathways to funding scientific software; constructing useful common metrics for crediting software stakeholders; identifying principles for sustainable software engineering design; reaching out to research software organizations around the world; and building communities for software sustainability. For each group, we include a point of contact and a landing page that can be used by those who want to join that group's future activities. The main challenge left by the workshop is to see if the groups will execute these activities that they have scheduled, and how the WSSSPE community can encourage this to happen

Report on the Third Workshop on Sustainable Software for Science: Practice and Experiences (WSSSPE3)

This report records and discusses the Third Workshop on Sustainable Software for Science: Practice and Experiences (WSSSPE3). The report includes a description of the keynote presentation of the workshop, which served as an overview of sustainable scientific software. It also summarizes a set of lightning talks in which speakers highlighted to-the-point lessons and challenges pertaining to sustaining scientific software. The final and main contribution of the report is a summary of the discussions, future steps, and future organization for a set of self-organized working groups on topics including developing pathways to funding scientific software; constructing useful common metrics for crediting software stakeholders; identifying principles for sustainable software engineering design; reaching out to research software organizations around the world; and building communities for software sustainability. For each group, we include a point of contact and a landing page that can be used by those who want to join that group’s future activities. The main challenge left by the workshop is to see if the groups will execute these activities that they have scheduled, and how the WSSSPE community can encourage this to happe