Papers › A reduced conjugate gradient basis method for fractional diffusion
A reduced conjugate gradient basis method for fractional diffusion
Yuwen Li, Ludmil T. Zikatanov, Cheng Zuo
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
This work is on a fast and accurate reduced basis method for solving discretized fractional elliptic partial differential equations (PDEs) of the form 𝒜ˢu=f by rational approximation. A direct computation of the action of such an approximation would require solving multiple (20∼30) large-scale sparse linear systems. Our method constructs the reduced basis using the first few directions obtained from the preconditioned conjugate gradient method applied to one of the linear systems. As shown in the theory and experiments, only a small number of directions (5∼10) are needed to approximately solve all large-scale systems on the reduced basis subspace. This reduces the computational cost dramatically because: (1) We only use one of the large-scale problems to construct the basis; and (2) all large-scale problems restricted to the subspace have much smaller sizes. We test our algorithms for fractional PDEs on a 3d Euclidean domain, a 2d surface, and random combinatorial graphs. We also use a novel approach to construct the rational approximation for the fractional power function by the orthogonal greedy algorithm (OGA).
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections