Randomized algorithms for estimating the trace of an implicit symmetric positive semi-definite matrix
نویسندگان
چکیده
منابع مشابه
A Trace Bound for Positive Definite Connected Integer Symmetric Matrices
Let A be a connected integer symmetric matrix, i.e., A = (aij) ∈ Mn(Z) for some n, A = AT , and the underlying graph (vertices corresponding to rows, with vertex i joined to vertex j if aij 6= 0) is connected. We show that if all the eigenvalues of A are strictly positive, then tr(A) ≥ 2n− 1. There are two striking corollaries. First, the analogue of the Schur-SiegelSmyth trace problem is solve...
متن کاملTrace minimization principles for positive semi-definite pencils
Article history: Received 7 September 2012 Accepted 4 December 2012 Available online 11 January 2013 Submitted by P. Šemrl AMS classification: 15A18 15A22 65F15
متن کاملA Randomized Algorithm for Approximating the Log Determinant of a Symmetric Positive Definite Matrix
We introduce a novel algorithm for approximating the logarithm of the determinant of a symmetric positive definite matrix. The algorithm is randomized and proceeds in two steps: first, it finds an approximation to the largest eigenvalue of the matrix after running a few iterations of the so-called “power method” from the numerical linear algebra literature. Then, using this information, it appr...
متن کاملSymmetric Positive Semi - Definite Solutions of Bax = and Dxc =
In this paper, a sufficient and necessary condition for the matrix equations B AX = and , D XC = where , , n m n m B A × × ∈ ∈ R R , p n C × ∈R and , p n D × ∈ R to have a common symmetric positive semi-definite solution X is established, and if it exists, a representation of the solution set X S is given. An optimal approximation between a given matrix n n X × ∈ R ~ and the affine subspace X S...
متن کاملEstimating the Largest Eigenvalue of a Positive Definite Matrix
The power method for computing the dominant eigenvector of a positive definite matrix will converge slowly when the dominant eigenvalue is poorly separated from the next largest eigenvalue. In this note it is shown that in spite of this slow convergence, the Rayleigh quotient will often give a good approximation to the dominant eigenvalue after a very few iterations-even when the order of the m...
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: Journal of the ACM
سال: 2011
ISSN: 0004-5411,1557-735X
DOI: 10.1145/1944345.1944349