Displaying similar documents to “Seventy years of Professor Miroslav Fiedler”

Condition numbers of Hessenberg companion matrices

Michael Cox, Kevin N. Vander Meulen, Adam Van Tuyl, Joseph Voskamp (2024)

Czechoslovak Mathematical Journal

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The Fiedler matrices are a large class of companion matrices that include the well-known Frobenius companion matrix. The Fiedler matrices are part of a larger class of companion matrices that can be characterized by a Hessenberg form. We demonstrate that the Hessenberg form of the Fiedler companion matrices provides a straight-forward way to compare the condition numbers of these matrices. We also show that there are other companion matrices which can provide a much smaller condition...

Pentadiagonal Companion Matrices

Brydon Eastman, Kevin N. Vander Meulen (2016)

Special Matrices

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The class of sparse companion matrices was recently characterized in terms of unit Hessenberg matrices. We determine which sparse companion matrices have the lowest bandwidth, that is, we characterize which sparse companion matrices are permutationally similar to a pentadiagonal matrix and describe how to find the permutation involved. In the process, we determine which of the Fiedler companion matrices are permutationally similar to a pentadiagonal matrix. We also describe how to find...

Elementary triangular matrices and inverses of k-Hessenberg and triangular matrices

Luis Verde-Star (2015)

Special Matrices

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We use elementary triangular matrices to obtain some factorization, multiplication, and inversion properties of triangular matrices. We also obtain explicit expressions for the inverses of strict k-Hessenberg matrices and banded matrices. Our results can be extended to the cases of block triangular and block Hessenberg matrices. An n × n lower triangular matrix is called elementary if it is of the form I + C, where I is the identity matrix and C is lower triangular and has all of its...