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MATRIX EQUATIONS AND CANONICAL FACTORIZATIONS

D. A. Bini, G. Latouche, and B. Meini

in Numerical Methods for Structured Markov Chains

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198527688
eISBN:
9780191713286
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198527688.003.0003
Subject:
Mathematics, Numerical Analysis

This chapter is concerned with infinite block Toeplitz matrices, their relationships with matrix power series and matrix Laurent power series, and the fundamental problem of solving matrix equations ... More


On the Time‐Series Approach to Econometric Model Building

David F. Hendry

in Econometrics: Alchemy or Science?: Essays in Econometric Methodology

Published in print:
2000
Published Online:
November 2003
ISBN:
9780198293545
eISBN:
9780191596391
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198293542.003.0006
Subject:
Economics and Finance, Econometrics

The ‘time‐series’ approach to econometrics is critically evaluated, and analytical test power response surfaces presented. Non‐stationarity, differencing and ‘error‐correction’ models (though not yet ... More


Computing complex zeros of polynomials and power series

Jean-Marc Couveignes

in Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM-176)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691142012
eISBN:
9781400839001
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691142012.003.0005
Subject:
Mathematics, Number Theory

The purpose of this chapter is twofold. First, it will prove two theorems (5.3.1 and 5.4.2) about the complexity of computing complex roots of polynomials and zeros of power series. The existence of ... More


Self-dual Poincaré Metrics

Charles Fefferman and C. Robin Graham

in The Ambient Metric (AM-178)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691153131
eISBN:
9781400840588
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153131.003.0005
Subject:
Mathematics, Geometry / Topology

As an application of the formal theory for Poincaré metrics, this chapter presents a formal power series proof of a result of LeBrun [LeB] asserting the existence and uniqueness of a real-analytic ... More


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