TY - JOUR

T1 - Algorithms for Wavelet Decomposition of of the Space of Hermite Type Splines

AU - Dem’yanovich, Yu K.

PY - 2019/10/7

Y1 - 2019/10/7

N2 - For the space of (not necessarily polynomial) Hermite type splines we develop algorithms for constructing the spline-wavelet decomposition provided that an arbitrary coarsening of a nonuniform spline-grid is a priori given. The construction is based on approximate relations guaranteeing the asymptotically optimal (with respect to the N-diameter of standard compact sets) approximate properties of this decomposition. We study the structure of restriction and extension matrices and prove that each of these matrices is the one-sided inverse of the transposed other. We propose the decomposition and reconstruction algorithms consisting of a small number of arithmetical actions.

AB - For the space of (not necessarily polynomial) Hermite type splines we develop algorithms for constructing the spline-wavelet decomposition provided that an arbitrary coarsening of a nonuniform spline-grid is a priori given. The construction is based on approximate relations guaranteeing the asymptotically optimal (with respect to the N-diameter of standard compact sets) approximate properties of this decomposition. We study the structure of restriction and extension matrices and prove that each of these matrices is the one-sided inverse of the transposed other. We propose the decomposition and reconstruction algorithms consisting of a small number of arithmetical actions.

UR - http://www.scopus.com/inward/record.url?scp=85071023146&partnerID=8YFLogxK

U2 - 10.1007/s10958-019-04470-z

DO - 10.1007/s10958-019-04470-z

M3 - Article

AN - SCOPUS:85071023146

VL - 242

SP - 133

EP - 148

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 1

ER -