READMEHEADmain

1 files changed, 16 insertions, 21 deletions

diff --git a/README.md b/README.md
index 2a65957..2609667 100644
--- a/README.md
+++ b/README.md
@@ -1,5 +1,4 @@
-This is a small C++ dense numerical linear algebra library, with a companion experiments directory 
-for evaluating performance.
+This is a small C++ dense numerical linear algebra library. 
 I mostly follow Trefethen & Bau, "Numerical Linear Algebra" and Golub & Van Loan, "Matrix 
 Computations."
 The implementation uses `NEON` SIMD on ARM64 systems when available.
@@ -11,7 +10,7 @@ The library is packaged as a C++20 named module (`linalgebra`):
 - CMake 4.1.x
 - Ninja
 - LLVM Clang ≥ 18 with libc++ (Homebrew LLVM 22 is what's tested; AppleClang
-  doesn't yet support module dependency scanning)
+  doesn't yet support C++20 module dependency scanning)
 
 ```bash
 cmake -S . -B build -G Ninja -DCMAKE_CXX_COMPILER=/opt/homebrew/opt/llvm/bin/clang++
@@ -56,25 +55,21 @@ ctest --test-dir build --output-on-failure
 - LU factorization with partial pivoting (`lu_factor`, `lu_solve`)
 - QR factorization — classical GS, modified GS, and Householder (`qr_classical_gs`, 
   `qr_modified_gs`, `qr_householder`)
-- Rank-revealing QR — Householder with column pivoting (`qr_colpiv`); reports numerical rank
-  and ensures |R(i,i)| ≥ |R(i+1,i+1)|
+- Rank-revealing QR — Householder with column pivoting (`qr_colpiv`)
 - Eigenvalue computation via QR iteration:
-  - Unshifted QR (`eigenvalues_unshifted`) — linear convergence, T&B Algorithm 28.1
-  - Wilkinson-shifted QR (`eigenvalues_shifted`) — typically cubic convergence, T&B Lecture 29
-  - Hessenberg + Givens QR (`eigenvalues_hessenberg`) — O(n²) per step after one O(n³) reduction; 
-    ~10–30× faster than `eigenvalues_shifted` for n ≥ 50
-  - Francis double-shift QR (`eigenvalues_francis`) — implicit bulge chasing on Hessenberg form;
-    handles complex conjugate eigenvalue pairs without complex arithmetic; robust subdiagonal +
-    2×2 block deflation with exceptional shifts (GVL §7.5)
+  - Unshifted QR (`eigenvalues_unshifted`)
+  - Wilkinson-shifted QR (`eigenvalues_shifted`)
+  - Hessenberg + Givens QR (`eigenvalues_hessenberg`)
+  - Francis double-shift QR (`eigenvalues_francis`)
 - Cholesky factorization (`cholesky_factor`, `cholesky_solve`) 
 - Symmetric tridiagonalization
-- Eigenvectors via inverse iteration (eigenvectors_inverse_iteration)
-- SVD — Golub-Kahan bidiagonalization + QR (svd)
-- Conjugate Gradient (solve_cg)
-- GMRES (solve_gmres)
-- BiCGSTAB (solve_bicgstab)
+- Eigenvectors via inverse iteration (`eigenvectors_inverse_iteration`)
+- SVD — Golub-Kahan bidiagonalization + QR (`svd`)
+- Conjugate Gradient (`solve_cg`)
+- GMRES (`solve_gmres`)
+- BiCGSTAB (`solve_bicgstab`)
 - Condition number estimation
-- Preconditioners (precond_jacobi, precond_ilu0)
-- Least squares solver (lstsq)
-- Arnoldi iteration (arnoldi)
-- Matrix exponential (expm)
+- Preconditioners (`precond_jacobi`, `precond_ilu0`)
+- Least squares solver (`lstsq`)
+- Arnoldi iteration (`arnoldi`)
+- Matrix exponential (`expm`)