A Note on Tractable State-Space Model for Symmetric Positive-Definite Matrices
نویسندگان
چکیده
منابع مشابه
DDtBe for Band Symmetric Positive Definite Matrices
We present a new parallel factorization for band symmetric positive definite (s.p.d) matrices and show some of its applications. Let A be a band s.p.d matrix of order n and half bandwidth m. We show how to factor A as A =DDt Be using approximately 4nm2 jp parallel operations where p =21: is the number of processors. Having this factorization, we improve the time to solve Ax = b by a factor of m...
متن کاملA 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 کاملGeometric Means in a Novel Vector Space Structure on Symmetric Positive-Definite Matrices
In this work we present a new generalization of the geometric mean of positive numbers on symmetric positive-definite matrices, called Log-Euclidean. The approach is based on two novel algebraic structures on symmetric positive-definite matrices: first, a lie group structure which is compatible with the usual algebraic properties of this matrix space; second, a new scalar multiplication that sm...
متن کاملDeconvolution Density Estimation on Spaces of Positive Definite Symmetric Matrices
Motivated by applications in microwave engineering and diffusion tensor imaging, we study the problem of deconvolution density estimation on the space of positive definite symmetric matrices. We develop a nonparametric estimator for the density function of a random sample of positive definite matrices. Our estimator is based on the Helgason-Fourier transform and its inversion, the natural tools...
متن کاملSupervised LogEuclidean Metric Learning for Symmetric Positive Definite Matrices
Metric learning has been shown to be highly effective to improve the performance of nearest neighbor classification. In this paper, we address the problem of metric learning for symmetric positive definite (SPD) matrices such as covariance matrices, which arise in many real-world applications. Naively using standard Mahalanobis metric learning methods under the Euclidean geometry for SPD matric...
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: SSRN Electronic Journal
سال: 2014
ISSN: 1556-5068
DOI: 10.2139/ssrn.2535282