Octave includes support for sparse matrices and MATPOWER makes use of them by default. It doesn't require any additional effort from me. In general, Octave can quite match MATLAB for performance, but it is typically not far off. Running it as WebAssembly also comes with a small performance penalty. I haven't run any benchmarks yet, but this can be expected to improve as browser vendors optimize their runtimes.

Octave is using UMFPACK to solve sparse systems of linear equations. There may be some performance to be gained by using KLU with AMD preordering.

I am interested to know how best to compile BLAS and LAPACK to WebAssembly. Traditionally, implementations optimized for a particular machine architecture are used to extract maximum performance. However, WebAssembly targets a stack-based conceptual machine. At present, I use LAPACK v3.4.2 and convert it to C with f2c before compiling to WebAssembly. It would be interesting to perform some benchmark tests against other implementations and compare across browsers.