TY - JOUR
T1 - Binomial matrices
AU - Boyd, Geoff
AU - Micchelli, Charles A.
AU - Strang, Gilbert
AU - Zhou, Ding-Xuan
PY - 2001
Y1 - 2001
N2 - Every s x s matrix A yields a composition map acting on polynomials on ℝs. Specifically, for every polynomial p we define the mapping CA by the formula (CAP)(x) := p(Ax), x ∈ ℝs. For each nonnegative integer n, homogeneous polynomials of degree n form an invariant subspace for CA. We let A(n) be the matrix representation of CA relative to the monomial basis and call A(n) a binomial matrix. This paper studies the asymptotic behavior of A(n) as n → ∞. The special case of 2 × 2 matrices A with the property that A2 = I corresponds to discrete Taylor series and motivated our original interest in binomial matrices.
AB - Every s x s matrix A yields a composition map acting on polynomials on ℝs. Specifically, for every polynomial p we define the mapping CA by the formula (CAP)(x) := p(Ax), x ∈ ℝs. For each nonnegative integer n, homogeneous polynomials of degree n form an invariant subspace for CA. We let A(n) be the matrix representation of CA relative to the monomial basis and call A(n) a binomial matrix. This paper studies the asymptotic behavior of A(n) as n → ∞. The special case of 2 × 2 matrices A with the property that A2 = I corresponds to discrete Taylor series and motivated our original interest in binomial matrices.
KW - Bernstein polynomials
KW - Binomial matrix
KW - De Casteljau subdivision
KW - Homogeneous polynomial
KW - Krawtchouk polynomials
KW - Permanents
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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-0035647576&origin=recordpage
U2 - 10.1023/A:1012207124894
DO - 10.1023/A:1012207124894
M3 - RGC 21 - Publication in refereed journal
VL - 14
SP - 379
EP - 391
JO - Advances in Computational Mathematics
JF - Advances in Computational Mathematics
SN - 1019-7168
IS - 4
ER -