Krylov Subspace Methods in Dynamical Sampling

Krylov Subspace Methods in Dynamical Sampling

Let B be an unknown linear evolution process on C ' `(Zd) driving an unknown initial state x and producing the states {Bx, ` = 0, 1, . . .} at different time levels. The problem under consideration in this paper is to find as much information as possible about B and x from the measurements Y = {x(i), Bx(i), . . . , Bix(i) : i ∈ Ω ⊂ Z}. If B is a “low-pass” convolution operator, we show that we ...

Preconditioned Krylov Subspace Methods for Sampling Multivariate Gaussian Distributions

A common problem in statistics is to compute sample vectors from a multivariate Gaussian distribution with zero mean and a given covariance matrix A. A canonical approach to the problem is to compute vectors of the form y = Sz, where S is the Cholesky factor or square root of A, and z is a standard normal vector. When A is large, such an approach becomes computationally expensive. This paper co...

Avoiding Krylov Subspace Methods

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Communication-avoiding Krylov subspace methods

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Krylov subspace methods in the electronic industry