Minimal Height Companion Matrices for Euclid Polynomials
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DOI: 10.1007/s11786-018-0364-2
Abstract: We define Euclid polynomials $$E_{k+1}(\lambda ) = E_{k}(\lambda )\left( E_{k}(\lambda ) - 1\right) + 1$$Ek+1(λ)=Ek(λ)Ek(λ)-1+1 and $$E_{1}(\lambda ) = \lambda + 1$$E1(λ)=λ+1 in analogy to Euclid numbers $$e_k = E_{k}(1)$$ek=Ek(1). We show how to construct… read more here.
Keywords: companion; height companion; minimal height; matrices euclid ... See more keywords
Companion matrices and Golden-Fibonacci sequences
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DOI: 10.1007/s12190-019-01240-7
Abstract: We assign a companion sequence to a given companion matrix. Given a companion matrix $$\mathbf{C}$$C, we make use of the associated companion sequence to provide a simple closed-form expression for $$\mathbf{C}^n$$Cn, the nth power of… read more here.
Keywords: matrix; golden fibonacci; companion; companion matrices ... See more keywords
Bounds on polynomial roots using intercyclic companion matrices
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DOI: 10.1016/j.laa.2017.11.002
Abstract: Abstract The Frobenius companion matrix, and more recently the Fiedler companion matrices, have been used to provide lower and upper bounds on the modulus of any root of a polynomial p ( x ) .… read more here.
Keywords: companion matrix; companion; bounds polynomial; companion matrices ... See more keywords