In July 2021, Sven Hammarling, Françoise Tisseur and I organized an online workshop New Directions in Numerical Linear Algebra and High Performance Computing. The workshop brought together researchers working in numerical linear algebra and high performance computing to discuss current developments and challenges in the light of evolving computer hardware. It was held to honour Jack Dongarra on the occasion of his 70th birthday. The workshop had been postponed from July 2020 as a result of the pandemic.

Videos of the talks are now available on the Numerical Linear Algebra Group’s YouTube channel and are included below. Slides for the talks are available on the workshop website.

**Sven Hammarling** (The University of Manchester), “Jack Dongarra”.

**Iain Duff** (STFC-RAL and CERFACS), “Jack”

**James Demmel** (University of California, Berkeley), “New Communication-Avoiding Algorithms, and Fixing Old Bugs in the BLAS and LAPACK”

**Piotr Luszczek** (University of Tennessee), “Numerical Methods and Across Scales, Precisions and Hardware Platforms”

**Cleve Moler** (MathWorks), “Computers That I Have Known”

**Yves Robert** (Ecole Normale Supérieure de Lyon), “25+ Years of Scheduling at ICL”

**Françoise Tisseur** (The University of Manchester), “Mixed Precision Tall and Thin QR Factorization with Applications”

**David Keyes** (King Abdullah University of Science and Technology), “Adaptive Nonlinear Preconditioning for PDEs with Error Bounds on Output Functionals”

**Zhaojun Bai** (University of California, Davis), “Many Eigenpair Computation Via Hotelling’S Deflation”,

**Ilse Ipsen** (North Carolina State University), “A Few Observations About Summation Algorithms”

**Erich Strohmaier** (TOP500), “TOP500 and Accidental Benchmarking”

**Nick Higham** (The University of Manchester), “Solving Dense Linear Systems: A Brief History and Future Directions ”

**Jack Dongarra** (University of Tennessee, Oak Ridge Laboratory and The University of Manchester), “Still Having Fun After 50 Years”,