Monotonicity and asymptotics of zeros of Sobolev type orthogonal polynomials: A general case
We investigate the location, monotonicity, and asymptotics of the zeros of the polynomials orthogonal with respect to the Sobolev type inner product〈p,q〉λ,c,j=∫abp(x)q(x)dμ(x)+λp(j)(c)q(j)(c), where μ is a positive Borel measure, λ⩾0, j∈Z+, and c∉(a,b). We prove that these zeros are monotonic functi...
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| Veröffentlicht in: | Applied numerical mathematics 2012-11, Vol.62 (11), p.1663-1671 |
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| container_title | Applied numerical mathematics |
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| creator | Castillo, Kenier Mello, Mirela V. Rafaeli, Fernando R. |
| description | We investigate the location, monotonicity, and asymptotics of the zeros of the polynomials orthogonal with respect to the Sobolev type inner product〈p,q〉λ,c,j=∫abp(x)q(x)dμ(x)+λp(j)(c)q(j)(c), where μ is a positive Borel measure, λ⩾0, j∈Z+, and c∉(a,b). We prove that these zeros are monotonic function of the parameter λ and establish their asymptotics when either λ converges to zero or to infinity. The precise location of the extreme zeros is also analyzed. |
| doi_str_mv | 10.1016/j.apnum.2012.05.006 |
| format | Article |
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We prove that these zeros are monotonic function of the parameter λ and establish their asymptotics when either λ converges to zero or to infinity. 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We prove that these zeros are monotonic function of the parameter λ and establish their asymptotics when either λ converges to zero or to infinity. 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| language | eng |
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| source | Elsevier ScienceDirect Journals Complete |
| subjects | Asymptotic behavior Asymptotic properties Infinity Mathematical analysis Mathematical models Monotonicity Orthogonal polynomials Position (location) Sobolev type inner product Zeros |
| title | Monotonicity and asymptotics of zeros of Sobolev type orthogonal polynomials: A general case |
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