https://www.reidatcheson.com/feed.xml

I propose here a way to factorize a sparse symmetric and indefinite matrix \(A\) with what I’ll call “Woodbury deferred pivots”, which allow us to retain a static execution plan even in the presence of numerical pivoting.

Choosing between OpenMP and oneTBB when linking oneMKL is an architectural choice between coordinated work-sharing and dynamic work-stealing.

In a recent post I gave intuition for the sparse Cholesky elimination tree by appealing to the task DAG and showed how it could be compressed into a tree in the sparse case.

Suppose you pose the following problem to me: solve a large sparse linear system Ax=b, where A and b are public and x is unknown.

Here I preview RatchesQR (note: contact me directly for access I have made the repository private to avoid LLM scraping without attribution), a low-memory sparse QR-factorization-based preconditioner that achieves good preconditioned GMRES convergence on…

I present here a deliberately unpleasant family for sparse linear solvers that operate only on an input sparse matrix.

In my recent post I motivated the elimination tree and gave a loose derivation from the Cholesky task DAG.

Here I derive the elimination tree for the right-looking sparse Cholesky algorithm, computing A = LL^T for a lower triangular L and sparse symmetric positive definite A.

Here I simulate a roughly 4x reduction in storage for a deflation basis with almost no change in iteration count on three test problems.

I explore how very small ML models might in some cases be better trained on CPU than GPU.

Here I look at “Compensated” arithmetic and its application to a small side-project CompensatedBLAS.