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Fast and Reliable Algorithms for High-Performance Numerical Linear Algebra

  • Full or part time
  • Application Deadline
    Applications accepted all year round
  • Funded PhD Project (Students Worldwide)
    Funded PhD Project (Students Worldwide)

Project Description

The project focuses on developing a new generation of numerical linear algebra algorithms that exploit current and future computers. The algorithms need to be fast and to be accompanied by rigorous error analysis to guarantee their reliability, even for the largest and most difficult problems. The target problems will be drawn from linear equations, linear least squares problems, eigenvalue problems, the singular value decomposition, and matrix function evaluation. These are the innermost kernels in many scientific and engineering applications---in particular, in data science and in machine learning---so it is essential that they are fast, accurate, and reliable.

A key aspect of this work is the exploitation of variable precision arithmetic. Low precision arithmetic is now available in hardware and is increasingly being used in machine learning and scientific computing more generally because of its speed, but its limited precision and narrow range require careful treatment. High precision (quadruple precision and above) is available in software and may be used in small amounts to speed up or stabilize an algorithm.

A strong background in numerical linear algebra and programming skills in MATLAB or a high level language are essential.

This project provides the opportunity to be part of a large and vibrant numerical linear algebra group that has several strongly committed industrial partners (see https://nla-group.org/).

Funding Notes

Open to all. Funding is available and would provide fees and maintenance at RCUK level for home/EU students, or a fees-only bursary for overseas students.

Related Subjects

How good is research at University of Manchester in Mathematical Sciences?

FTE Category A staff submitted: 54.40

Research output data provided by the Research Excellence Framework (REF)

Click here to see the results for all UK universities

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