On computing Schur functions and series thereof
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Author(s)
Chan, Cy
Drensky, Vesselin
Edelman, Alan
Kan, Raymond
Koev, Plamen
Date Issued
October 20, 2018
Publisher
Springer US
Version
Author's final manuscript
Abstract
Abstract
In this paper, we present two new algorithms for computing all Schur functions
$$s_\kappa (x_1,\ldots ,x_n)$$
s
κ
(
x
1
,
…
,
x
n
)
for partitions
$$\kappa $$
κ
such that
$$|\kappa |\le N$$
|
κ
|
≤
N
. For nonnegative arguments,
$$x_1,\ldots ,x_n$$
x
1
,
…
,
x
n
, both algorithms are subtraction-free and thus each Schur function is computed to high relative accuracy in floating point arithmetic. The cost of each algorithm per Schur function is
$$\mathscr {O}(n^2)$$
O
(
n
2
)
.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s10801-018-0846-y
