SIAM News Blog

Report of the XXI Householder Symposium on Numerical Linear Algebra

By Leonardo Robol and Francesco Tudisco

The Mediterranean atmosphere of Hotel Sierra Silvana—located in the southeastern Apulia region of Italy—served as the backdrop of the 21st Householder Symposium on Numerical Linear Algebra, which commenced from June 12-17, 2022. The conference continued the Gatlinburg Symposia tradition that was established by Alston Householder, who organized the first such gathering in the Great Smoky Mountains of Tennessee. This meeting unexpectedly took place five years after the 20th symposium in Blacksburg, Va.; the 21st iteration was originally scheduled for 2020, but it was canceled in light of the global COVID-19 pandemic.

The Householder Symposium is considered one of (if not the) most important conferences on numerical linear algebra in the world. It has a peculiar structure in that participation is by invitation only, the number of attendees is limited to roughly 150 delegates, and the location is typically remote to reduce distractions and favor interactions among all participants. Such interactions were facilitated by the symposium’s traditional random seating assignment at all lunches and dinners.

The steering committee—chaired by Heike Fassbender (Technical University of Braunschweig) and responsible for the meeting’s scientific components—was composed of Zhaojun Bai (University of California, Davis), David Bindel (Cornell University), James Demmel (University of California, Berkeley), Zlatko Drmać (University of Zagreb), Sherry Li (Lawrence Berkeley National Laboratory), Volker Mehrmann (Technical University of Berlin), James Nagy (Emory University), Valeria Simoncini (University of Bologna), and Andrew Wathen (University of Oxford).

The conference program comprised 115 lectures, including 23 plenary talks and three addresses by recipients of Householder Prizes. Following the custom of previous Householder symposia, an evening poster session by the pool saw lively participation and discussion by conference attendees. Prior to the poolside session, presenters participated in a poster blitz wherein they had one minute—strictly enforced—to introduce a few highlights from their posters and solicit the interest of attendees.

Topic Highlights and the Householder Prize

The symposium featured an exciting blend of modern numerical linear algebra topics, such as spectra of infinite-dimensional operators, nonlinear eigenvalue problems, functions of matrices and preconditioning, uncertainty quantification and data assimilation, and low-rank approximation methods. Randomized linear algebra played a key role in several of these contributions; it was well-represented as both an autonomous topic and an increasingly common method for addressing uncertainties, handling reduced communication, and computing at extreme scales.

Several talks dealt with the numerics behind spectra computations for infinite-dimensional operators. The richness of infinite-dimensional spectra—which may comprise a continuous as well as a discrete part—when compared with matrices and finite-dimensional operators makes this problem inherently challenging to treat via a finite number of operations.

In line with tradition, the best poster award and the Householder Prizes were presented at the conference banquet. The best poster prize was shared by Elizabeth Newman (Emory University) for her poster on “Train Like a (Var)Pro: Efficient Training of Neural Networks with Variable Projections” and Maike Meier (University of Oxford) for her poster on “Randomized Algorithms for Tikhonov Regularization in Linear Least Squares.”

The Householder Prize is bestowed every three years to the best Ph.D. thesis in numerical linear algebra, with submissions from around the world. Because the 2020 symposium was canceled, both the 2020 and 2022 prizes were awarded during the conference banquet.

The two recipients of the 2020 Householder Prize were Estelle Massart (Ph.D. from Université catholique de Louvain in Belgium) with a thesis on “Data Fitting on Positive-semidefinite Matrix Manifolds” and Stefano Massei (Ph.D. from Scuola Normale Superiore di Pisa in Italy) for his thesis on “Exploiting Rank Structures in the Numerical Solution of Markov Chains and Matrix Functions.”

Two individuals also received 2020 honorable mentions: Pawan Goyal (Ph.D. from Otto von Guericke University in Germany) for his thesis on “System-theoretic Model Order Reduction for Bilinear and Quadratic-Bilinear Systems” and Theo Mary (Ph.D. from University of Toulouse in France) for his thesis on “Block Low-rank Multifrontal Solvers: Complexity, Performance, and Scalability.”

The 2022 Householder Prize was awarded to Heather Wilber (Ph.D. from Cornell University) for her thesis on “Computing Numerically with Rational Functions.” Honorable mentions were given to María del Carmen Quintana Ponce (Ph.D. from Universidad Carlos III de Madrid in Spain) for her thesis on “Linearizations of Rational Matrices” and Sung Woo Jeong (Ph.D. from Massachusetts Institute of Technology) for his work on “Linear Algebra, Random Matrices and Lie Theory.”

The Householder Prize is completely financed by donations that are collected during the previous symposium’s banquet; due to the COVID-19 pandemic, offers for the 2022 prize were collected online.

Italian Hospitality

The local organizing committee, led by Nicola Mastronardi (National Research Council in Italy), deserves hearty congratulations for a successful meeting.

Most of the meals commenced in the dining hall of Hotel Sierra Silvana, with the exception of a few dinner events that took place in the garden area’s marquee near the pool. Live music accompanied the welcome reception and social dinner, and a variety of locally produced dishes were served at all meals.

Continuing another Householder tradition, one afternoon was devoted to local excursions. Participants had the option of traveling to the Baroque city of Lecce in Italy’s Salentine peninsula region, visiting the nearby UNESCO World Heritage Site of Alberobello, or relaxing at the beach.

The Householder Symposium was sponsored by several organizations and companies. GNCS/INdAM (Gruppo Nazionale per il Calcolo Scientifico), the International Linear Algebra Society, MathWorks, SIAM, and the University of Bologna all contributed to the success of this meeting; their financial support is very much appreciated.

We already look towards the next Householder Symposium with great enthusiasm. The forthcoming 2025 meeting—which is organized by David Bindel, Anil Damle, and Alex Townsend—will take place in June 2025 at Cornell University.

Photos courtesy of Antonio Mastronardi and Nicola Mastronardi.

  Leonardo Robol is an assistant professor in the Department of Mathematics at the University of Pisa in Italy. 
  Francesco Tudisco is an associate professor in the School of Mathematics at Gran Sasso Science Institute in Italy. 


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