Research

Principles of Informatics Research Division

NAKATSUKASA Yuji
Principles of Informatics Research Division Associate Professor
Doctoral Degrees: Ph.D.
Research Fields: Mathematical Informatics

Introduction of research by science writer

From a kid who liked math to an applied mathematician

I enjoyed math from a young age, and I was attracted to pure mathematics. When I became a graduate student, I became interested in numerical linear algebra and numeric calculations that frequently employ matrices (rectangular arrays of numbers) representing specific data and by which I can imagine something useful (such as data analyses and computer simulations), as opposed to pure math, which often deals with highly abstract objects.

I had always been interested in going overseas, and encouraged by my family and academic supervisor, I went to study at the University of California, Davis, where I worked on eigenvalue problems in numerical linear algebra for five years. As an example, when a matrix is decomposed using the singular value decomposition (a type of eigenvalue problem; expressed as a simple matrix multiplication), the matrix can often be represented using little memory, and this can be applied to data compression. I also worked on the development of algorithms that achieve high compression efficiency using the singular value decomposition.

Linear algebra is the foundation of applied mathematics

After University of California, Davis, I went as a postdoc to the University of Manchester, UK, where I continued my research related to numerical linear algebra. The joint research that I carried out with two researchers who I met there was very enjoyable, and I became more enthusiastic than ever about my research. Joint research and discussions with other researchers gave me confidence, and I got the sense that I could make it as an academic.

Then, I worked as an assistant professor at the University of Tokyo, where I studied and conducted research on optimization. The range of applications for optimization is large, to the point that one could say that all problems are optimization problems. For example, optimization can be used to solve everyday issues such as how to maximize sales or how to minimize manufacturing costs. Specifically, I started working on a class of optimization problems that can be solved by computing eigenvalues, and this includes problems that were regarded as difficult.

Broadly, two problems are solved in numerical linear algebra--the linear equation Ax=b and the eigenvalue problem Ax=λx--and these are necessary in all areas of applied mathematics. However, I believe that there are still many applications for eigenvalues in particular that are yet to be explored.

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The common roots of two functions of two variables can be calculated using eigenvalues.

The common roots of two functions of two variables can be calculated using eigenvalues.

Also, function approximation theory is almost always behind numeric calculations, including eigenvalue problems (although this perspective is not common knowledge, even among experts). For example, with the open source software Chebfun (a project I was involved in as a researcher at the University of Oxford), we can perform numeric calculations with functions at high speed and with high accuracy, and to find highly accurate optimal values. In the future, I would like to continue working on theory and algorithms for numerical computing based on function approximation theory.

Becoming a world leader in numerical linear algebra

Since joining NII, I have been carrying out research on my own initiative. I aim to do research that will hopefully make a difference in the world by helping to solve important problems that need to be resolved today, including the application of eigenvalue problems to other fields, interdisciplinary research that connects fields of applied math, and (although I have hardly touched on these areas before) application to machine learning and big data analysis.
I would also like to become a world leader in numerical linear algebra by inviting collaborations for cutting-edge research on numeric calculations, hosting workshops through the NII Shonan Meetings, and supervising students and researchers from Japan and overseas.

Memories

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At the University of Manchester, I had a fulfilling and enjoyable experience as a researcher with my collaborators, Alex (left) and Vanni (center). Even today, they are friends who continue to inspire me, and I always keep an eye on the research that they and other researchers are involved in.

I think that numeric calculations will become increasingly important in the future, and I hope to contribute to solving important problems by engaging passionately in discussions and working enthusiastically on research.


Interview/text by Tsutomu Sahara

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