Recurrence relation for biorthogonal polynomials |
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| Affiliation: | 1. Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia;2. Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan;1. Department of Mathematics and Computer Science, National University of Lesotho, P.O. Roma 180, Lesotho;2. Faculty of Mathematics, Kyushu University, 744 Motooka, Nishiku, Fukuoka 819-0395, Japan |
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| Abstract: | We use a geometric approach to obtain a recurrence relation for two families of biorthogonal polynomials associated to a nonsingular, strongly regular matrix M. We propose a “look-ahead procedure” for computing the biorthogonal polynomials when M has singular or ill-conditioned leading principal submatrices. These polynomials lead to two recursive triangular factorizations for the inverse of a nonsingular matrix M which is not necessarily strongly regular. |
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