Krylov Basis-Size Const-Generic Convention

Summary

Krylov subspace methods that build up a basis of a fixed maximum size expose that size as a const K: usize (Lanczos, Arnoldi) or const M: usize (GMRES(m) restart size) type parameter directly on the public function, following the notation standard in the numerical linear algebra literature.

Scope

Applies to any current or future Krylov subspace method whose basis (or restart) size is known at compile time — Lanczos and Arnoldi iterations, and the restart parameter of GMRES(m). Does not apply to power_iteration/inverse_power_iteration, which have no basis of growing size to bound. Does not introduce a new trait; it extends the existing minimal [[static-dynamic-storage-trait]] the same way every other generic algorithm in the crate already does.

Decision

const K: usize names the Lanczos/Arnoldi basis size, and const M: usize names the GMRES(m) restart size — the same symbols the literature uses for each, rather than a single shared name across both algorithm families or a crate-invented one.

This size is a direct const-generic type parameter on the public function signature, not hidden behind a wrapper type. Matrix types already expose their dimensions as const generics throughout the public API (StaticMatrix<T, const R: usize, const C: usize>), so a basis size expressed the same way is consistent with how callers already read every other compile-time size in this crate; wrapping it would introduce a second convention for the same kind of information with no offsetting benefit.

The const generic is an extension of the existing narrow Storage trait used to write generic algorithms once against both static and dynamic storage, not a new trait — consistent with the crate’s one-pattern-reused-across-algorithms approach already established for Krylov and other generic numerical code.

Constraints

• K and M name the basis/restart size specifically for Lanczos/Arnoldi and GMRES(m) respectively; a different Krylov method with a differently-named parameter in its own literature uses that name instead, rather than being forced onto K/M for consistency’s own sake.
• The basis/restart size is exposed as a direct type parameter on the public function, never hidden behind a wrapper type, matching how matrix dimensions are already exposed elsewhere in the public API.
• No new trait is introduced to support this; any capability the algorithms need beyond what the existing storage trait exposes is added to that trait only when a concrete algorithm needs it, not speculatively.

Status

Partially implemented. Lanczos now exists and exposes its basis size as const K: usize, establishing the pattern this convention describes. Arnoldi and GMRES(m) do not exist in the crate yet.