Numerical Linear Algebra Toolkit

Purpose

Provides high-performance numerical linear algebra operations for scientific computing and mathematical analysis.

Capabilities

• Matrix decompositions (LU, QR, SVD, Cholesky, Schur)
• Eigenvalue/eigenvector computation
• Sparse matrix operations
• Iterative solvers (CG, GMRES, BiCGSTAB)
• Condition number estimation
• Error analysis and bounds

Usage Guidelines

1. Decomposition Selection: Choose appropriate factorization for the problem
2. Sparsity Exploitation: Use sparse formats for large sparse matrices
3. Iterative Methods: Apply iterative solvers for very large systems
4. Conditioning: Assess and monitor condition numbers

Tools/Libraries

• LAPACK
• BLAS
• SuiteSparse
• Eigen