پديد آورنده :
شفيعي، محمد
عنوان :
كران هايي براي مقادير ويژه اكسترمال رده اي خاص از ماتريس هاي سه قطره اي متقارن
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
علوم رياضي - رياضي كاربردي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
يادداشت :
ص.ع.به فارسي و انگليسي
استاد راهنما :
رضا مختاري
استاد مشاور :
مريم شمس سولاري
توصيفگر ها :
ماتريس سه قطري تاپليتز , ماتريس متقارن , مقدار تكين
تاريخ نمايه سازي :
21/10/93
استاد داور :
محمود منجگاني، مهدي تاتاري
چكيده انگليسي :
Bounds for the extremal eigenvalues of aclass of symmetric tridiagonal matrices Mohamad Sha ei m sha ei@math iut ac ir 2014 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Reza Mokhtari mokhtari@cc iut ac ir Advisor Dr Maryam Shams Solary shamssolary@pnu ac ir 2010 MSC 05C15 53C42 Keywords Tridiagonal matrices Toeplitz Symmetric matrices Eigenvalues Singular values Extremal eigenvalues AbstractThese days obtaining an optimal bound for smallest and or largest eigenvalues or singular values of agiven matrix is one of the important and notable issues Although great achievements for the estima tion of eigenvalues or singular values have been discovered bounds obtained so far are not satisfactoryyet Recently Buchholzer et al H Buchholzer C Kanzow Bounds for the extremal eigenvalues ofa class of symmetric tridiagonal matrices with applications Linear Algebra and its Applications 436 2012 1837 1849 have been extracted some sharp bounds for the extremal eigenvalues of a class ofsymmetric tridiagonal matrices with Toeplits structure which destroyed by perturbing two elementson each o diagonal They could also obtain a lower bound for the smallest singular value of symmet ric or asymmetric Toeplitz tridiagonal positive de nite matrices and apply these bounds in solvingan advection di usion partial di erential equation and shown that such bounds are very useful andapplicable In fact they could apply their results to the discretization of a partial di erential equationwhere matrices arise that can be decomposed as a Kronecker product of tridiagonal matrices of thementioned structure It must be pointed out that the key idea of their work is based on the behaviorof obtained xed points of a recursive equation The main theoretical results contained in their workare depending on the relative absolute sizes of the matrix entries Results show that their boundsare more appropriated rather than previous bounds At the beginning of this thesis after preparing
استاد راهنما :
رضا مختاري
استاد مشاور :
مريم شمس سولاري
استاد داور :
محمود منجگاني، مهدي تاتاري
