LAPACK-like linear algebra

This chapter describes all of the linear algebra operations which are not basic enough to fall within the BLAS (Basic Linear Algebra Subprograms) framework. In particular, algorithms which would traditionally have fallen into the domain of LAPACK (Linear Algebra PACKage), such as factorizations and matrix decompositions, are placed here.

• Reduction to condensed form
  • Hermitian to tridiagonal
  • Square to Hessenberg
  • General to bidiagonal
  • References
• Factorizations
  • Cholesky factorization
  • LDL factorization
  • LU factorization
  • LQ factorization
  • QR factorization
  • RQ factorization
  • Generalized QR factorization
  • Generalized RQ factorization
  • Interpolative Decomposition (ID)
  • Skeleton decomposition
  • References
• Spectral analysis
  • Hermitian tridiagonal eigensolvers
  • Hermitian eigensolvers
  • Skew-Hermitian eigensolvers
  • Hermitian generalized-definite eigensolvers
  • Hermitian SVD
  • SVD
  • Polar decomposition
  • Schur decomposition
  • Specialized eigensolvers
  • Pseudospectra
  • References
• Matrix functions
  • Direct inversion
  • Hermitian functions
  • Pseudoinverse
  • Square root
  • Sign
• Matrix properties
  • Condition number
  • Determinant
  • Inertia
  • Matrix norms
  • Trace
• Linear solvers
  • Linear solve
  • Symmetric solve
  • Hermitian solve
  • HPD solve
  • Multi-shift Hessenberg solves
  • References
• Euclidean minimization
  • Least Squares
  • Tikhonov regularization
  • Ridge regression
  • General (Gauss-Markov) Linear Model
  • Equality-constrained Least Squares
  • References
• Permutations
  • Permutation vectors
  • Pivot sequences
  • Converting pivot sequences to permutations
• Reflectors
  • Householder reflectors
  • Hyperbolic reflectors
• Utilities
  • Median
  • Sorting