TRICG & TRIMR: support warm-start with ldiv=true

[timholy]

This addresses some potential inconsistencies in tricg and trimr in
the case ldiv=true:

• docs: fixes the statement about the relationship between E/F and
  M/N
• docs: describes the residual-norm in terms of E/F rather than
  M/N (only the former are unambiguous, given the problem statement)
• adds support for warm-starting when ldiv=true for arbitrary M/N

NOTE: this is a WIP as trimr has not yet been modified. Once we settle on the tricg changes, I'll port the same changes to trimr.

[timholy]

To clarify, this is ready for review despite me having switched it to "draft." I did that just because it shouldn't be merged until I make commensurate changes to trimr.

[codecov]

Codecov Report

❌ Patch coverage is 81.25000% with 6 lines in your changes missing coverage. Please review.
✅ Project coverage is 97.64%. Comparing base (9536ef7) to head (3f3455b).
⚠️ Report is 122 commits behind head on main.

Files with missing lines	Patch %	Lines
src/trimr.jl	62.50%	6 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1043      +/-   ##
==========================================
+ Coverage   94.68%   97.64%   +2.96%     
==========================================
  Files          45       50       +5     
  Lines        8027    10027    +2000     
==========================================
+ Hits         7600     9791    +2191     
+ Misses        427      236     -191     

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[timholy]

I also included a fix for #1076 for these two methods. Something similar may be needed for the others.

[Copilot]

Pull request overview

This PR updates the TriCG/TriMR saddle-point solvers to better support warm-starting when ldiv=true, and clarifies the documentation around how the weighting operators E/F relate to the user-provided preconditioners M/N.

Changes:

• TriCG docstring updated to describe E/F consistently for both ldiv=false and ldiv=true, and to restate residual norm weighting in terms of E/F.
• TriCG and TriMR relax the “warm-start with preconditioners not supported” restriction when ldiv=true, and rework initialization so warm-start can reinitialize with the shifted RHS.
• Added a TriCG warm-start regression test for ldiv=true with a non-identity N.

Reviewed changes

Copilot reviewed 3 out of 3 changed files in this pull request and generated 9 comments.

File	Description
src/tricg.jl	Doc clarifications for E/F vs M/N; enables warm-start path when ldiv=true; adjusts initialization sequence.
src/trimr.jl	Mirrors the warm-start gating/initialization changes for ldiv=true (despite PR note calling TrimR “not yet modified”).
test/test_warm_start.jl	Adds a warm-start round-trip test for tricg(...; N, ldiv=true) to validate the new behavior.

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[timholy]

I believe this is ready for merging. Since it is about warm-starting, I also went ahead and implemented a fix for #1076 for these two methods.