4423

4173

كارشناسي ارشد

رياضي، كاربردي ،آناليز عددي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1387

[هفت]،137،[II]ص.

ص. ع به: فارسي و انگليسي

رضا مختاري

محمود منجگاني

23/01/1388

محمد رضا مختار زاده ، مهدي تاتاري

رياضي

ID4173

به فارسي و انگليسي: قابل رويت در نسخه ديجيتال

Constructive Methods in Solving Real Nonnegative Inverse Eigenvalue Problem Maryam Mohammadi m mohammadi@math iut ac ir October 2008 Master of Science Thesis Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor Dr Reza Mokhtari mokhtari@cc iut ac ir Advisor Dr Mahmood Manjegani manjgani@cc iut ac ir Department Graduate Program Coordinator Dr Rasoul Nasr Isfahani isfahani@cc iut ac ir Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran AbstractIn this thesis we present an extended account of the real nonnegative inverse eigenvalueproblem RNIEP based on an article by Carlos Marijuan Miriam Pisonero and RicardoL Soto A map of su cient conditions for the real nonnegative inverse eigenvalue problem This problem is originated from the inverse eigenvalue problem IEP which has a remarkablevariety of applications in the mathematical modelling The nonnegative inverse eigenvalueproblem NIEP is the problem of determining necessary and su cient conditions for a listof complex numbers to be the spectrum of an entrywise nonnegative matrix This problemhas only been solved for n 3 by Loewy and London in 1978 and for the cases n 4 andn 5 for matrices of trace zero by Reams in 1996 La ey and Meehan in 1999 For theNIEP in addition to the 3 basic necessary conditions we have the JLL inequality due toJohnson Loewy and London in 1978 and a re nement of it in the case of trace zero due toLa ey and Meehan in 1998 When is a list of real numbers the problem changes to theRNIEP This problem has only been solved for n 4 by Loewy and London However anumber of su cient conditions have been obtained which some of them have constructiveproofs in the sense that one can can explicitly construct nonnegative matrices realizing theprescribed real spectrum This thesis has been arranged as follows We begin by introducing the notation and basicconcepts and some important applications of the IEP We determine the necessary conditionsunder which a NIEP has a solution in chapter 2 In Chapter 3 we probe the NIEP in specialsolved cases which are quoted before Chapter 4 contains the su cient conditions havingconstructive proofs in solving the RNIEP which most of them are due to Ricardo L Soto We also state some su cient conditions having constructive proofs in solving the symmetricnonnegative inverse eigenvalue problem SNIEP in chapter 5 The corresponding algorithmsof these chapters are also given separately Finally we collect the corresponding matlabprograms of the algorithms in appendix 1

رضا مختاري

محمود منجگاني

محمد رضا مختار زاده ، مهدي تاتاري