We propose an algorithm for the numerical solution of the Lur’e equations in the bounded real and positive real lemma for stable systems. The recently developed ADI iteration for algebraic Riccati equations is generalized to Lur’e equations. The algorithm provides approximate solutions in low-rank factored form. We prove that the sequence of approximate solutions is monotonically increasing wit...

Efficient representations and solutions for large decision problems with continuous and discrete variables are among the most important challenges faced by the designers of automated decision support systems. In this paper, we describe a novel hybrid factored Markov decision process (MDP) model that allows for a compact representation of these problems, and a new hybrid approximate linear progr...

Exact monitoring in dynamic Bayesian net­ works is intractable, so approximate algo­ rithms are necessary. This paper presents a new family of approximate monitoring al­ gorithms that combine the best qualities of the particle filtering and Boyen-Koller meth­ ods. Our algorithms maintain an approxi­ mate representation the belief state in the form of sets of factored particles, that cor­ respon...

The most widely used approach for solving the polynomial eigenvalue problem P (λ)x = (∑m i=0 λ Ai ) x = 0 in n × n matrices Ai is to linearize to produce a larger order pencil L(λ) = λX + Y , whose eigensystem is then found by any method for generalized eigenproblems. For a given polynomial P , infinitely many linearizations L exist and approximate eigenpairs of P computed via linearization can...

We present a chart of structured backward errors for approximate eigenpairs of singly and doubly structured eigenvalue problems. We aim to give, wherever possible, formulae that are inexpensive to compute so that they can be used routinely in practice. We identify a number of problems for which the structured backward error is within a factor √ 2 of the unstructured backward error. This paper c...