Transcription of Gershgorin’s Circle Theorem for Estimating the Eigenvalues ...
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Gershgorin’s Circle Theorem for Estimating the Eigenvalues ...
Gershgorin s Circle Theorem forEstimating the Eigenvalues of aMatrix with Known Error BoundsAuthor:DavidMarquisAdvisors:Profes sor HansDe MoorDr. KathrynPorterReader:Dr. MichaelNathansonMay 15, 2016 Figure 1: Semyon Aranovich GershgorinAbstractSquare matrices are characterized by their Eigenvalues , so we would like to be able to producethe Eigenvalues for any square matrix. Cofactor expansion is an algorithm used to producewhat is known as the characteristic polynomial of a matrixA, the roots of which are theeigenvalues ofA. However, the algorithm for cofactor expansion is computationally intensiveand as the output is annthdegree polynomial, we do not have any guaranteed method tofind the roots for large Aranovich Gershgorin (1901-1933), was a mathematician who worked mainly inthe study of differential equations.
Square matrices are characterized by their eigenvalues, so we would like to be able to produce the eigenvalues for any square matrix. Cofactor expansion is an algorithm used to produce what is known as the characteristic polynomial of a matrix A, the roots of …
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