On a generalized matrix approximation problem in the spectral norm

• Abstract in UndeterminedIn this paper theoretical results regarding a generalized minimum rank matrix approximation problem in the spectral norm are presented. An alternative solution expression for the generalized matrix approximation problem is obtained. This alternative expression provides a simple characterization of the achievableminimum rank, which is shown to be the same as the optimal objective value of the classical problem considered by Eckart–Young–Schmidt–Mirsky, as long as the generalized problem is feasible. In addition, this paper provides a result on a constrained version of the matrix approximation problem, establishing that the later problem is solvable via singular value decomposition.

Subject headings

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

Keyword

matrix approximation

rank minimization

singular value decomposition

Publication and Content Type

art (subject category)

ref (subject category)