Poisson equation with iterative refinement.
Float64 establishes the reference. Float32 exposes the precision floor. The mixed path recomputes the outer residual in Float64 while solving corrections in Float32.
Numerical systems, mixed-precision research,
and accelerator infrastructure for next-generation
simulation and AI-scale computation.
ShardNet publishes working numerical experiments, failure boundaries, and machine-readable receipts instead of hiding behind benchmark claims.
Float64 establishes the reference. Float32 exposes the precision floor. The mixed path recomputes the outer residual in Float64 while solving corrections in Float32.
Hilbert systems become progressively hostile to finite precision. Mixed refinement helps, then fails sharply once the Float32 factorization is no longer a useful correction operator.
The work spans precision systems, scientific kernels, and scale-out execution. Hardware results stay marked pending until they actually run.
Define the accuracy target and residual checks before choosing a precision path.
Place the actual computation against memory and accelerator constraints.
Validate accuracy and execution behavior on the hardware that runs it.
Decomposition, refinement, reconstruction, and error-aware execution with explicit accuracy contracts.
Read the research ↗Dense, sparse, spectral, stencil, reduction, and solver kernels for modern matrix engines and memory hierarchies.
Experiment plan ↗Multi-GPU decomposition, collective behavior, memory placement, and scaling measured as part of the algorithm.
Discuss a workload ↗