Algorithms for the Polar Decomposition

Perturbation Bounds for the Polar Decomposition

Let M n (F) denote the space of matrices over the eld F. Given A2 M n (F) deene jAj (A A) 1=2 and U(A) AjAj ?1 assuming A is nonsingular. Let 1 (A) 2 (A) n (A) 0 denote the ordered singular values of A. We obtain majorization results relating the singular values of U(A + A) ? U(A) and those of A and A. In particular we show that if A; A2 M n (R) and 1 ((A) < n (A) then for any unitarily invaria...

Biconjugate Decomposition Using ABS Algorithms

The Canonical Generalized Polar Decomposition

The polar decomposition of a square matrix has been generalized by several authors to scalar products on Rn or Cn given by a bilinear or sesquilinear form. Previous work has focused mainly on the case of square matrices, sometimes with the assumption of a Hermitian scalar product. We introduce the canonical generalized polar decomposition A = WS, defined for general m × n matrices A, where W is...

Polar Decomposition for P-adic Symmetric Spaces

Let G be the group of k-points of a connected reductive k-group and H a symmetric subgroup associated to an involution σ of G. We prove a polar decomposition G = KAH for the symmetric space G/H over any local field k of characteristic not 2. Here K is a compact subset of G and A is a finite union of groups Ai which are the k-points of maximal (k, σ)-split tori, one for each H-conjugacy class. T...

Finding the polar decomposition of a matrix by an efficient iterative method

Theobjective in this paper to study and present a new iterative method possessing high convergence order for calculating the polar decompostion of a matrix. To do this, it is shown that the new scheme is convergent and has high convergence. The analytical results are upheld via numerical simulations and comparisons.