Computing a logarithm of a unitary matrix with general spectrum
نویسندگان
چکیده
منابع مشابه
Computing the Logarithm of a Symmetric Positive Deenite Matrix
A numerical method for computing the logarithm of a symmetric positive dee-nite matrix is developed in this paper. It is based on reducing the original matrix to a tridiagonal matrix by orthogonal similarity transformations and applying Pad e approximations to the logarithm of the tridiagonal matrix. Theoretical studies and numerical experiments indicate that the method is quite eecient when th...
متن کاملA fixed point iteration for computing the matrix logarithm
In various areas of applied numerics, the problem of calculating the logarithm of a matrix A emerges. Since series expansions of the logarithm usually do not converge well for matrices far away from the identity, the standard numerical method calculates successive square roots. In this article, a new algorithm is presented that relies on the computation of successive matrix exponentials. Conver...
متن کاملReturn to the Middle Ages: A Half-Angle Iteration for the Logarithm of a Unitary Matrix
If A is unitary then A = eiH = cos H + i sin H where H is Hermitian. We examine the problem of approximating H . The standard approach to approximating logarithms is to take successive square roots until A1/2 n is close to the identity and then apply a Padé approximation to log A = 2n log A1/2 n . For the unitary problem we have A1/2 n = cos(H/2n) + i sin(H/2n) which suggests the use of halfang...
متن کاملComputing Wiener and hyper–Wiener indices of unitary Cayley graphs
The unitary Cayley graph Xn has vertex set Zn = {0, 1,…, n-1} and vertices u and v are adjacent, if gcd(uv, n) = 1. In [A. Ilić, The energy of unitary Cayley graphs, Linear Algebra Appl. 431 (2009) 1881–1889], the energy of unitary Cayley graphs is computed. In this paper the Wiener and hyperWiener index of Xn is computed.
متن کاملdeterminant of the hankel matrix with binomial entries
abstract in this thesis at first we comput the determinant of hankel matrix with enteries a_k (x)=?_(m=0)^k??((2k+2-m)¦(k-m)) x^m ? by using a new operator, ? and by writing and solving differential equation of order two at points x=2 and x=-2 . also we show that this determinant under k-binomial transformation is invariant.
15 صفحه اولذخیره 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: Numerical Linear Algebra with Applications
سال: 2014
ISSN: 1070-5325
DOI: 10.1002/nla.1927