mpgeslir: IR solver

mpgeslir(AF::MPFact, b; reporting=false, verbose=true)

I do not export this function. The idea is that you use mplu and do not touch either the constructor or the solver directly.

Use a multi-precision factorization to solve a linear system with plain vanilla iterative refinement.

This version is analogous to A\b and combines the factorization and the solve. You start with MPA=MPArray(A) and then pass MPA to mpgeslir and combine the factorization and the solve.

You can also get the multiprecision factorization directly with

MPF=mplu(A)

and then pass MPF to mpgeslir.

I use this to get some timing results and it's also convenient if you want to do factor and solve in one statement.

You can also get this with x = MPA\b.

If you set the kwarg reporting to true you can get the IR residual history. The output of

x = MPA\b

Use a multi-precision factorization to solve a linear system with plain vanilla iterative refinement.

MPFact is a union of all the MultiPrecision factorizations in the package. The triangular solver will dispatch on the various types depending on how the interprecision transfers get done.

mpgeslir(MPA::MPArray, b; reporting = false, verbose = true)

I do not export this function. The idea is that you use mpglu and do not touch either the constructor or the solver directly.

Use a multi-precision factorization to solve a linear system with plain vanilla iterative refinement.

This version is analogous to A\b and combines the factorization and the solve. You start with MPA=MPArray(A) and then pass MPA to mpgeslir and combine the factorization and the solve.

You can also get the multiprecision factorization directly with

MPF=mplu(A)

and then pass MPF to mpgeslir.

I use this to get some timing results and it's also convenient if you want to do factor and solve in one statement.

You can also get this with x = MPA\b.

If you set the kwarg reporting to true you can get the IR residual history. The output of

x = MPA\b

or

x=MPF\b

is the solition. The output of

mout = \(MPA,b; reporting=true)

or

mout = \(MPF,b; reporting=true)

is a structure. mpout.sol is the solution. mpout.rhist is the residual history. mpout also contains the datatypes TW for high precision and TF for low precision.

Example

julia> using MultiPrecisionArrays.Examples

julia> N=4096; A = I - 800.0 * Gmat(N); b=ones(N);

julia> MPF=mplu(A);

julia> mout=\(MPF, b; reporting=true);

julia> mout.rhist
6-element Vector{Float64}:
 1.00000e+00
 5.36483e-02
 1.57977e-05
 5.10232e-09
 7.76756e-12
 9.90008e-12

# Stagnation after four IR iterations

julia> [mout.TW mout.TF]
1×2 Matrix{DataType}:
 Float64  Float32