Rational orthogonal approximations to orthogonal matrices
نویسندگان
چکیده
منابع مشابه
Computational Geometry: Theory and Applications 7:25-35, 1997. Rational Orthogonal Approximations to Orthogonal Matrices
Several algorithms are presented for approximating an orthogonal rotation matrix M in three dimensions by an orthogonal matrix with rational entries. The rst algorithm generates an approximation M2(M;) with accuracy and 2b+2-bit numerators and a common 2b+2-bit denominator (bit-size 2b+2), where b = d?lg e (2 ?b). The second algorithm uses basis reduction to generate an approximation M (M;) wit...
متن کاملOrthogonal Rational Functions and Structured Matrices
The space of all proper rational functions with prescribed poles is considered. Given a set of points zi in the complex plane and the weights wi, we define the discrete inner product
متن کاملSemidefinite approximations for quadratic programs over orthogonal matrices
Finding global optimum of a non-convex quadratic function is in general a very difficult task even when the feasible set is a polyhedron. We show that when the feasible set of a quadratic problem consists of orthogonal matrices from Rn×k, then we can transform it into a semidefinite program in matrices of order kn which has the same optimal value. This opens new possibilities to get good lower ...
متن کاملAlgorithm for generating orthogonal matrices with rational elements
Special orthogonal n × n matrices with rational elements form the group SO(n, Q), where Q is the field of rational numbers. A theorem describing the structure of an arbitrary matrix from this group is proved. This theorem yields an algorithm for generating such matrices by means of random number routines.
متن کاملOrthogonal Rational Functions with real coefficients and semiseparable matrices
When one wants to use Orthogonal Rational Functions (ORFs) in system identification or control theory, it is important to be able to avoid complex calculations. In this paper we study ORFs whose numerator and denominator polynomial have real coefficients. These ORFs with real coefficients (RORFs) appear when the poles and the interpolation points appear in complex conjugate pairs, which is a na...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computational Geometry
سال: 1997
ISSN: 0925-7721
DOI: 10.1016/0925-7721(95)00048-8