Sketched-and-recycled FOM (srFOM)

A library that implements recycled FOM (rFOM) and sketched-and-recycled FOM (srFOM) proposed in [1] for sequences of matrix functions $f(A^{(i)})\mathbf{b}^{(i)}$ with slowly changing matrices $A^{(i)}$ and/or vectors $\mathbf{b}^{(i)}$.

Tests

All test scripts used to generate the plots in [1] can be found in the "tests" folder. These files are:

test_quad_v_closed.m: compares the closed-form formulation of recycled FOM against the quadrature-based implementation presented in [2].

test_inv_sqrt_fixed_m.m: runs the inverse square root example, and generates a plot of the error for each method obtained after a fixed number of Arnoldi iterations.

test_inv_sqrt_fixed_reltol.m: runs the inverse square root example, and generates a plot of the Arnoldi cycle length required for each method to converge.

test_exp.m: runs the matrix exponential example.

test_inv.m: runs the inverse function example.

References

[1] L. Burke and S. Güttel. Krylov subspace recycling with randomized sketching for matrix functions, arXiv:2308.02290, 2023.

[2] L. Burke, A. Frommer, G. Ramirez-Hidalgo, and K. M. Soodhalter. Krylov subspace recycling for matrix functions, arXiv:2209.14163, 2022.