Schur algorithm
E506855
The Schur algorithm is a recursive procedure in complex analysis and operator theory used to construct and analyze Schur functions, playing a key role in interpolation problems and system theory.
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical algorithm
ⓘ
method in complex analysis ⓘ method in operator theory ⓘ recursive procedure ⓘ |
| appliesTo | Schur functions ⓘ |
| assumes |
function analytic in the open unit disk
ⓘ
function bounded by 1 in modulus on the unit disk ⓘ |
| basedOn | Schur transformation NERFINISHED ⓘ |
| characterizes | contractive analytic functions on the unit disk ⓘ |
| domain | unit disk ⓘ |
| field |
complex analysis
ⓘ
control theory ⓘ function theory ⓘ operator theory ⓘ system theory ⓘ |
| generalizationOf | continued fraction expansions for analytic functions ⓘ |
| historicalPeriod | early 20th century ⓘ |
| input | Schur function ⓘ |
| mapsTo | unit ball of H-infinity ⓘ |
| namedAfter | Issai Schur NERFINISHED ⓘ |
| output |
sequence of Schur parameters
ⓘ
sequence of contractive coefficients ⓘ |
| property |
iteratively reduces degree or complexity of a Schur function
ⓘ
preserves contractivity at each step ⓘ |
| relatedTo |
Hardy spaces
NERFINISHED
ⓘ
Herglotz functions NERFINISHED ⓘ Nevanlinna–Pick interpolation problem NERFINISHED ⓘ Schur complement NERFINISHED ⓘ inner–outer factorization ⓘ transfer functions of linear systems ⓘ |
| usedFor |
Carathéodory–Fejér interpolation
NERFINISHED
ⓘ
Nevanlinna–Pick interpolation NERFINISHED ⓘ analysis of Schur functions ⓘ computation of Schur parameters ⓘ computation of reflection coefficients ⓘ construction of Schur functions ⓘ factorization of analytic functions ⓘ interpolation problems ⓘ model reduction in system theory ⓘ realization theory in system theory ⓘ signal processing ⓘ spectral estimation ⓘ |
| usedIn |
discrete-time system theory
ⓘ
operator model theory ⓘ orthogonal polynomials on the unit circle ⓘ prediction theory of stationary processes ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.