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Improved linear equation solving #764

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pietercollins opened this issue Oct 19, 2023 · 0 comments
Open

Improved linear equation solving #764

pietercollins opened this issue Oct 19, 2023 · 0 comments
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algebra Algebra module enhancement Something new or different that is an improvement

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@pietercollins
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Our current solver for linear equations computes a matrix inverse using Gaussian elimination. Especially for validated matrices, this leads to large errors due to the dependency effect. We should instead implement direct solution for approximate matrices, and a preconditioned solver for validated matrices.

We should also implement a solver using a-posteriori error analysis as proposed by Rump.

Finally, we should provide a LinearSolver interface to abstract details of linear algebra solver methods.
@pietercollins pietercollins added enhancement Something new or different that is an improvement algebra Algebra module labels Oct 19, 2023
@pietercollins pietercollins self-assigned this Oct 19, 2023
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algebra Algebra module enhancement Something new or different that is an improvement
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