The boundary of the numerical range of matrix polynomials

The higher rank numerical range of nonnegative matrices

“…Analogous statement to Proposition 14 for the "sharp points" of Λ j (L(λ)) we may confirm taking into consideration Theorem 1.4 in [17].…”

Numerical approximation of the boundary of numerical range of matrix polynomials

“…The suggested reference on F (A) and its properties is [2]. The last decade, the numerical range W (P ) in (2) has attracted attention, and several results have been obtained (see e.g., [1,4,5,6,7,9,10,11,12,13,16]). These results are helpful in investigating and understanding matrix polynomials, and lead to interesting applications of the numerical range on the spectral analysis, the factorization and the stability of matrix polynomials, [4,11,16].…”

“…These results are helpful in investigating and understanding matrix polynomials, and lead to interesting applications of the numerical range on the spectral analysis, the factorization and the stability of matrix polynomials, [4,11,16]. To facilitate the presentation, some basic geometrical properties of W (P ) are given below, [6,7,8,9,10].…”

Ανωτέρου Βαθμού Αριθμητικά Πεδία Μη Αρνητικών Πινάκων Και Πολυωνυμικών Πινάκων

“…(1.3) To w(L(λ)) parousisthke apì touc C.K. Li kai L. Rodman [34] kai sth sunèqeia, melet jhke ekten¸c apì touc M. Adm, I. Maroul kai P. Yarrko stic ergasÐec [1,44,45,50], kajìson oi poluwnumikoÐ pÐnakec apoteloÔn qr simo er-galeÐo sthn epÐlush susthmtwn sun jwn diaforik¸n exis¸sewn se probl mata thc upologistik c qhmeÐac kai thc moriak c biologÐac [15,18].…”

“…. , k. ArkeÐ mìno na apodeÐxoume oti gia opoiod pote dÐsko S(z 0 , ε), me ε > 0, to shmeÐo z 0 ikanopoieÐ thn isìthta Re(e iθ z 0 ) = max { Re z : e −iθ z ∈ Λ j (Aλ − B) ∩ S(z 0 , ε) }MporoÔme na diatup¸soume ènan anlogo isqurismì me thn Prìtash 4.13 gia ta {gwniak shmeÐa} tou Λ j (L(λ)), lambnontac upìyin to je¸rhma 1.4 sthn ergasÐa[45].…”