TY - JOUR

T1 - D-Optimal Designs for a Multivariate Polynomial Model

AU - Шпилев, Петр Валерьевич

AU - Куча, Елизавета Сергеевна

PY - 2025/6/1

Y1 - 2025/6/1

N2 - Abstract: For a multivariate polynomial regression model, the problem of constructing a D-optimal design on a symmetric (relative to the origin) design region is studied. Based on the symmetry property, an approach, which reduces the computational complexity of constructing the optimal design, is proposed. For the case of an asymmetric region, an algorithm for constructing D-optimal designs for a multivariate quadratic polynomial model without a constant term is developed. This model has significant practical importance and can be used in various applications, such as calculating the service life of road surfaces depending on a variety of factors.

AB - Abstract: For a multivariate polynomial regression model, the problem of constructing a D-optimal design on a symmetric (relative to the origin) design region is studied. Based on the symmetry property, an approach, which reduces the computational complexity of constructing the optimal design, is proposed. For the case of an asymmetric region, an algorithm for constructing D-optimal designs for a multivariate quadratic polynomial model without a constant term is developed. This model has significant practical importance and can be used in various applications, such as calculating the service life of road surfaces depending on a variety of factors.

KW - D‑optimal designs

KW - multivariate regression models

KW - polynomial regression models without a constant term

UR - https://www.mendeley.com/catalogue/886434e1-00ce-388d-97dc-285fc704c2f7/

U2 - 10.1134/s1063454125700219

DO - 10.1134/s1063454125700219

M3 - Article

VL - 58

SP - 232

EP - 238

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 2

ER -