Optimization algorithms on matrix manifolds - Absil, P.A; Absil, P.A; Mahony,R; Sepulchre,R (Princeton University Press, 2008)
Keywords: Affine space; Algorithm; Algorithms; Analytic function; Complex projective space; Computation; Computational problem; COMPUTERS / Computer Science; Conjugate gradient method; Constrained optimization; Directional derivative; Eigenvalue algorithm; Eigenvalues and eigenvectors; Equation; Euclidean vector; Finsler manifold; Fixed-point theorem; Gauss–Newton algorithm; Geometry; Global optimization; Gradient descent; Inclusion map; Invariant subspace; Invariant subspace problem; Invertible matrix; Iteration; Iterative method; Levenberg–Marquardt algorithm; Line search; Linear algebra; Linear map; Linear space (geometry); Linear subspace; Local convergence; Manifold; Mathematical optimization; MATHEMATICS; MATHEMATICS / Applied; Matrices; Matrix (mathematics); Matrix decomposition; Newton's method; Normed vector space; Numerical analysis; Numerical integration; Numerical linear algebra; Optimization problem; Principal component analysis; Product topology; Projection (linear algebra); Quadratic equation; Quasi-Newton method; Quotient space (topology); Rate of convergence; Rayleigh quotient; Rayleigh quotient iteration; Real projective space; Riemannian geometry; Riemannian manifold; Riemannian submanifold; Row and column spaces; Scale invariance; Simultaneous equations; Stiefel manifold; Submanifold; Submersion (mathematics); Subset; Subspace topology; Tangent space; Tangent vector; Taylor's theorem; Technology; Technology & Engineering / Engineering (General); Theorem; Topological space; Topology; Vector space; Subset; Euclidean vector; Iterative method; Projection (linear algebra); Matrix (mathematics); Tangent vector; Gradient descent; Vector space; Eigenvalue algorithm; Eigenvalues and eigenvectors; Invertible matrix; Tangent space; Finsler manifold; Real projective space; Numerical linear algebra; Invariant subspace problem; Topology; Subspace topology; Riemannian manifold; Matrix decomposition; Algorithm; Complex projective space; Gauss–Newton algorithm