### Pat Keast (1942-2016)

Patrick (Pat) Keast, retired professor, Department of Mathematics and Statistics, Dalhousie University, passed away suddenly at his home in Halifax on Monday, July 25, 2016,

at the age of 73. He is survived by his wife Kathleen, whom he met in high school, and sons Liam (Brenda) and James (Stephanie) and his grandchildren, Isaac, Kate and Ella.

Pat was born in Broxburn, Scotland, on August 2nd, 1942. In 1960, upon leaving St. Mary’s Academy in the neighboring town of Bathgate as dux of his class, he entered the University of Edinburgh, and began an outstanding undergraduate career. In 1964, he graduated with a first class honours degree in mathematics and received the Napier Medal and Gangadhar Balwant Gadgil Prize in Mathematics awarded to the most distinguished student in Mathematics in the Final Honours examination. He then joined the Mathematics Department at St. Andrews University and while an assistant lecturer there completed a Ph.D. in Mathematics in 1967 under the supervision of Andrew (Ron) Mitchell.

Pat spent the academic year 1968-1969 at the University of Toronto (U of T) as a visitor in the Computer Science Department. In 1970, he immigrated to Canada to take up a regular faculty position at U of T, splitting his time between teaching in the undergraduate program at the U of T Scarborough College campus, and teaching graduate courses and supervising graduate students at the U of T St. George campus.

In 1983, Pat moved to Dalhousie University (Dal) where he joined the newly establishedDivision of Computing Science in the Mathematics, Statistics, and Computer Science Department. He completed his career in the Mathematics and Statistics Department at Dal, retiring in 2007. During his 24 years at Dal, he taught many undergraduate students, supervised numerous graduate students in both mathematics and computer science, and held several administrative positions, including Department Chair. Pat was a highly respected teacher; former students have spoken of the outstanding attention that he gave to his teaching and to his students.

Throughout his career, Pat maintained an active research program in numerical analysis and scientific computing supported by NSERC grants. His Ph.D. thesis and earliest publications focused on numerical methods for solving partial differential equations, an area that he revisited later in his career. After his move to Toronto, he spent several summers at Argonne National Laboratory which led to his work on multidimensional quadrature with James Lyness. In 1985, Pat directed a NATO Advanced Research Workshop on Numerical Integration at Dalhousie University in which many of the leading researchers in the area of numerical quadrature from around the world participated.

From the early eighties, a central aspect of Pat’s research was the development of robust numerical software packages, which he accomplished with colleagues and graduate students. His early achievements in this area were in the formulation and implementation of efficient methods for the solution of a class of structured linear systems known as almost block diagonal (ABD). Such systems arise in all well-known methods for solving boundary value ordinary differential equations (BVODEs) and in certain spline collocation techniques for solving partial differential equations (PDEs). He then embedded these solvers in commonly used packages for solving BVODEs and time-dependent PDEs in one space dimension with resulting efficiencies.

A fundamental limitation of the early 1D PDE collocation packages was that only the temporal error was controlled. From the late nineties until the end of his research career, the development of high quality numerical software for the error controlled numerical solution of 1D PDEs became a central theme in Pat’s work. Along with colleagues, he developed the first software package implementing a collocation solver that computed both spatial and temporal error controlled numerical solutions of general classes of systems of 1D PDEs. Subsequently he contributed to the development of refinements of this package which is now in its third edition. All of the numerical software packages in which Pat was involved are available in the highly respected Collected Algorithms of the Association for Computing Machinery. Moreover, codes based on the ABD solvers appear in the NAG software library.

It was not all work and no play with Pat. He was a devoted family man and greatly enjoyed having his sons, both of whom are computer scientists, and their families living in close proximity to his home. He was very active in the church communities of St. Pius X and St. Benedict’s in Halifax especially through his work with the St. Vincent de Paul Society. Throughout his life, he was passionate about cycling. While at U of T, he regularly cycled between U of T Scarborough and U of T St. George, and subsequently he cycled around much of Nova Scotia in addition to commuting to Dal by bike. On summer vacations to visit family in Scotland, his bike accompanied him and he thoroughly enjoyed cycling in central Scotland with his two brothers. It also accompanied him to Argonne where he had more than one mishap that took him to an emergency room.

Many will long remember Pat’s delightful sense of humour, oft described by family members as “quirky”. Not as well-known was his uncanny ability to create limericks with remarkable ease. Several years ago, he considered writing a book, each chapter of which would begin with a limerick, an example of which is the following.

A simple eigenvalue named psi Was perturbed by a small amount, phi. The change was sufficient To make its eigenvector deficient And the condition of the matrix quite high.Unfortunately the book did not get past the limerick stage. 🙂

Pat will be greatly missed by family, friends and the communities of which he was a vital part.

Paul Muir and Graeme Fairweather, with contributions from Ronnie Keast