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[documentation] Fix references
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@amontoison
amontoison committed Sep 24, 2023
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12 changes: 6 additions & 6 deletions docs/src/block_processes.md
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Original file line number Diff line number Diff line change
Expand Up @@ -25,7 +25,7 @@ T_{k+1,k} =
\end{bmatrix}.
```

The function [`hermitian_lanczos`](@ref hermitian_lanczos) returns $V_{k+1}$, $\Psi_1$ and $T_{k+1,k}$.
The function [`hermitian_lanczos`](@ref hermitian_lanczos(::Any, ::AbstractMatrix{FC}, ::Int) where FC <: (Union{Complex{T}, T} where T <: AbstractFloat)) returns $V_{k+1}$, $\Psi_1$ and $T_{k+1,k}$.

```@docs
hermitian_lanczos(::Any, ::AbstractMatrix{FC}, ::Int) where FC <: (Union{Complex{T}, T} where T <: AbstractFloat)
Expand Down Expand Up @@ -66,7 +66,7 @@ T_{k,k+1}^H =
\end{bmatrix}.
```

The function [`nonhermitian_lanczos`](@ref nonhermitian_lanczos) returns $V_{k+1}$, $\Psi_1$, $T_{k+1,k}$, $U_{k+1}$ $\Phi_1^H$ and $T_{k,k+1}^H$.
The function [`nonhermitian_lanczos`](@ref nonhermitian_lanczos(::Any, ::AbstractMatrix{FC}, ::AbstractMatrix{FC}, ::Int) where FC <: (Union{Complex{T}, T} where T <: AbstractFloat)) returns $V_{k+1}$, $\Psi_1$, $T_{k+1,k}$, $U_{k+1}$ $\Phi_1^H$ and $T_{k,k+1}^H$.

```@docs
nonhermitian_lanczos(::Any, ::AbstractMatrix{FC}, ::AbstractMatrix{FC}, ::Int) where FC <: (Union{Complex{T}, T} where T <: AbstractFloat)
Expand Down Expand Up @@ -97,7 +97,7 @@ H_{k+1,k} =
\end{bmatrix}.
```

The function [`arnoldi`](@ref arnoldi) returns $V_{k+1}$, $\Gamma$, and $H_{k+1,k}$.
The function [`arnoldi`](@ref arnoldi(::Any, ::AbstractMatrix{FC}, ::Int) where FC <: (Union{Complex{T}, T} where T <: AbstractFloat)) returns $V_{k+1}$, $\Gamma$, and $H_{k+1,k}$.

```@docs
arnoldi(::Any, ::AbstractMatrix{FC}, ::Int) where FC <: (Union{Complex{T}, T} where T <: AbstractFloat)
Expand Down Expand Up @@ -138,7 +138,7 @@ L_{k+1}^H =
\end{bmatrix}.
```

The function [`golub_kahan`](@ref golub_kahan) returns $V_{k+1}$, $U_{k+1}$, $\Psi_1$ and $L_{k+1}$.
The function [`golub_kahan`](@ref golub_kahan(::Any, ::AbstractMatrix{FC}, ::Int) where FC <: (Union{Complex{T}, T} where T <: AbstractFloat)) returns $V_{k+1}$, $U_{k+1}$, $\Psi_1$ and $L_{k+1}$.

```@docs
golub_kahan(::Any, ::AbstractMatrix{FC}, ::Int) where FC <: (Union{Complex{T}, T} where T <: AbstractFloat)
Expand Down Expand Up @@ -179,7 +179,7 @@ T_{k,k+1}^H =
\end{bmatrix}.
```

The function [`saunders_simon_yip`](@ref saunders_simon_yip) returns $V_{k+1}$, $\Psi_1$, $T_{k+1,k}$, $U_{k+1}$, $\Phi_1^H$ and $T_{k,k+1}^H$.
The function [`saunders_simon_yip`](@ref saunders_simon_yip(::Any, ::AbstractMatrix{FC}, ::AbstractMatrix{FC}, ::Int) where FC <: (Union{Complex{T}, T} where T <: AbstractFloat)) returns $V_{k+1}$, $\Psi_1$, $T_{k+1,k}$, $U_{k+1}$, $\Phi_1^H$ and $T_{k,k+1}^H$.

```@docs
saunders_simon_yip(::Any, ::AbstractMatrix{FC}, ::AbstractMatrix{FC}, ::Int) where FC <: (Union{Complex{T}, T} where T <: AbstractFloat)
Expand Down Expand Up @@ -220,7 +220,7 @@ F_{k+1,k} =
\end{bmatrix}.
```

The function [`montoison_orban`](@ref montoison_orban) returns $V_{k+1}$, $\Gamma$, $H_{k+1,k}$, $U_{k+1}$, $\Lambda$, and $F_{k+1,k}$.
The function [`montoison_orban`](@ref montoison_orban(::Any, ::Any, ::AbstractMatrix{FC}, ::AbstractMatrix{FC}, ::Int) where FC <: (Union{Complex{T}, T} where T <: AbstractFloat)) returns $V_{k+1}$, $\Gamma$, $H_{k+1,k}$, $U_{k+1}$, $\Lambda$, and $F_{k+1,k}$.

```@docs
montoison_orban(::Any, ::Any, ::AbstractMatrix{FC}, ::AbstractMatrix{FC}, ::Int) where FC <: (Union{Complex{T}, T} where T <: AbstractFloat)
Expand Down
12 changes: 6 additions & 6 deletions docs/src/processes.md
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Original file line number Diff line number Diff line change
Expand Up @@ -89,7 +89,7 @@ T_{k+1,k} =
```
Note that depending on how we normalize the vectors that compose $V_k$, $T_{k+1,k}$ can be a real tridiagonal matrix even if $A$ is a complex matrix.

The function [`hermitian_lanczos`](@ref hermitian_lanczos) returns $V_{k+1}$ and $T_{k+1,k}$.
The function [`hermitian_lanczos`](@ref hermitian_lanczos(::Any, ::AbstractVector{FC}, ::Int) where FC <: (Union{Complex{T}, T} where T <: AbstractFloat)) returns $V_{k+1}$ and $T_{k+1,k}$.

Related methods: [`SYMMLQ`](@ref symmlq), [`CG`](@ref cg), [`CR`](@ref cr), [`CAR`](@ref car), [`MINRES`](@ref minres), [`MINRES-QLP`](@ref minres_qlp), [`MINARES`](@ref minares), [`CGLS`](@ref cgls), [`CRLS`](@ref crls), [`CGNE`](@ref cgne), [`CRMR`](@ref crmr), [`CG-LANCZOS`](@ref cg_lanczos) and [`CG-LANCZOS-SHIFT`](@ref cg_lanczos_shift).

Expand Down Expand Up @@ -131,7 +131,7 @@ T_{k,k+1} =
\end{bmatrix}.
```

The function [`nonhermitian_lanczos`](@ref nonhermitian_lanczos) returns $V_{k+1}$, $T_{k+1,k}$, $U_{k+1}$ and $T_{k,k+1}^H$.
The function [`nonhermitian_lanczos`](@ref nonhermitian_lanczos(::Any, ::AbstractVector{FC}, ::AbstractVector{FC}, ::Int) where FC <: (Union{Complex{T}, T} where T <: AbstractFloat)) returns $V_{k+1}$, $T_{k+1,k}$, $U_{k+1}$ and $T_{k,k+1}^H$.

Related methods: [`BiLQ`](@ref bilq), [`QMR`](@ref qmr), [`BiLQR`](@ref bilqr), [`CGS`](@ref cgs) and [`BICGSTAB`](@ref bicgstab).

Expand Down Expand Up @@ -197,7 +197,7 @@ H_{k+1,k} =
\end{bmatrix}.
```

The function [`arnoldi`](@ref arnoldi) returns $V_{k+1}$ and $H_{k+1,k}$.
The function [`arnoldi`](@ref arnoldi(::Any, ::AbstractVector{FC}, ::Int) where FC <: (Union{Complex{T}, T} where T <: AbstractFloat)) returns $V_{k+1}$ and $H_{k+1,k}$.

Related methods: [`DIOM`](@ref diom), [`FOM`](@ref fom), [`DQGMRES`](@ref dqgmres), [`GMRES`](@ref gmres) and [`FGMRES`](@ref fgmres).

Expand Down Expand Up @@ -246,7 +246,7 @@ B_k =
```
Note that depending on how we normalize the vectors that compose $V_k$ and $U_k$, $L_k$ can be a real bidiagonal matrix even if $A$ is a complex matrix.

The function [`golub_kahan`](@ref golub_kahan) returns $V_{k+1}$, $U_{k+1}$ and $L_{k+1}$.
The function [`golub_kahan`](@ref golub_kahan(::Any, ::AbstractVector{FC}, ::Int) where FC <: (Union{Complex{T}, T} where T <: AbstractFloat)) returns $V_{k+1}$, $U_{k+1}$ and $L_{k+1}$.

Related methods: [`LNLQ`](@ref lnlq), [`CRAIG`](@ref craig), [`CRAIGMR`](@ref craigmr), [`LSLQ`](@ref lslq), [`LSQR`](@ref lsqr) and [`LSMR`](@ref lsmr).

Expand Down Expand Up @@ -292,7 +292,7 @@ T_{k,k+1} =
\end{bmatrix}.
```

The function [`saunders_simon_yip`](@ref saunders_simon_yip) returns $V_{k+1}$, $T_{k+1,k}$, $U_{k+1}$ and $T_{k,k+1}^H$.
The function [`saunders_simon_yip`](@ref saunders_simon_yip(::Any, ::AbstractVector{FC}, ::AbstractVector{FC}, ::Int) where FC <: (Union{Complex{T}, T} where T <: AbstractFloat)) returns $V_{k+1}$, $T_{k+1,k}$, $U_{k+1}$ and $T_{k,k+1}^H$.

Related methods: [`USYMLQ`](@ref usymlq), [`USYMQR`](@ref usymqr), [`TriLQR`](@ref trilqr), [`TriCG`](@ref tricg) and [`TriMR`](@ref trimr).

Expand Down Expand Up @@ -347,7 +347,7 @@ F_{k+1,k} =
\end{bmatrix}.
```

The function [`montoison_orban`](@ref montoison_orban) returns $V_{k+1}$, $H_{k+1,k}$, $U_{k+1}$ and $F_{k+1,k}$.
The function [`montoison_orban`](@ref montoison_orban(::Any, ::Any, ::AbstractVector{FC}, ::AbstractVector{FC}, ::Int) where FC <: (Union{Complex{T}, T} where T <: AbstractFloat)) returns $V_{k+1}$, $H_{k+1,k}$, $U_{k+1}$ and $F_{k+1,k}$.

Related methods: [`GPMR`](@ref gpmr).

Expand Down

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