The Generalized Minimal Residual methods (GMRES) for the solution of general square linear systems Ax = b is often combined with a preconditioner to improve the convergence speed and the overall computing performance of the method. Successful mixed precision implementations for the application of the preconditioner inside GMRES have been previously proposed: certain strategy prescribes to apply...
We develop a mixed-precision iterative refinement framework for solving low-rank Lyapunov matrix equations AX + XA* + W = 0, where W = LL* or W = LSL*. Via rounding error analysis of the algorithms we derive sufficient conditions for the attainable normwise residuals in different precision settings and show how the algorithmic parameters should be chosen. Using the sign function Newton iteration as the...
Polynomial matrices arise naturally in a variety of signal processing, control, communication, and MIMO system applications. Similar to conventional matrices, they require structured decompositions—such as eigenvalue decomposition (EVD), singular value decomposition (SVD), and QR decomposition—to enable optimal solutions in many practical problems. These factorizations play a critical role in broadband data compaction, MIMO-OFDM system design,...
1985 saw a release of one of the most important standards in computing, the IEEE 754-1985 floating-point standard, which is at the foundation of most modern computing systems in use today. Two revisions of the standard, IEEE 754-2008 and IEEE 754-2019, have since been released. A working group for the IEEE 754-2029 is already assembled...
