Hermite's formula for vector polynomial interpolation with applications to structured matrices

1998 ◽  
Vol 70 (3-4) ◽  
pp. 331-345 ◽  
Author(s):  
Georg Heinig ◽  
Fadhel Al-Musallam
Keyword(s):  
Polynomial Interpolation ◽  
Structured Matrices ◽  
Vector Polynomial

scholarly journals Global Properties of Eigenvalues of Parametric Rank One Perturbations for Unstructured and Structured Matrices

2021 ◽  
Vol 15 (3) ◽  
Author(s):  
André C. M. Ran ◽  
Michał Wojtylak
Keyword(s):  
Unit Circle ◽  
Structured Matrices ◽  
Additional Structure ◽  
General Properties ◽  
Global Properties ◽  
Classes Of Matrices ◽  
Rank One

AbstractGeneral properties of eigenvalues of $$A+\tau uv^*$$ A + τ u v ∗ as functions of $$\tau \in {\mathbb {C} }$$ τ ∈ C or $$\tau \in {\mathbb {R} }$$ τ ∈ R or $$\tau ={{\,\mathrm{{e}}\,}}^{{{\,\mathrm{{i}}\,}}\theta }$$ τ = e i θ on the unit circle are considered. In particular, the problem of existence of global analytic formulas for eigenvalues is addressed. Furthermore, the limits of eigenvalues with $$\tau \rightarrow \infty $$ τ → ∞ are discussed in detail. The following classes of matrices are considered: complex (without additional structure), real (without additional structure), complex H-selfadjoint and real J-Hamiltonian.

scholarly journals Profiled Horn Antenna with Wideband Capability Targeting Sub-THz Applications

Electronics ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 412
Author(s):  
Jay Gupta ◽  
Dhaval Pujara ◽  
Jorge Teniente
Keyword(s):  
Hermite Polynomial ◽  
Polynomial Interpolation ◽  
Horn Antenna ◽  
Submillimeter Wavelengths ◽  
Thz Applications ◽  
Millimeter And Submillimeter Wavelengths ◽  
Better Than

This paper proposes a wideband profiled horn antenna designed using the piecewise biarc Hermite polynomial interpolation and validated experimentally at 55 GHz. The proposed design proves S11 and directivity better than −22 dB and 25.5 dB across the entire band and only needs 3 node points if compared with the well-known spline profiled horn antenna. Our design makes use of an increasing radius and hence does not present non-accessible regions from the aperture, allowing its fabrication with electro erosion techniques especially suitable for millimeter and submillimeter wavelengths.

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