The D-optimal saturated designs of order 22

Chasiotis, Vasilis; Kounias, Stratis; Farmakis, Nikolaos

doi:10.1016/j.disc.2017.09.005

Cited by 4 publications

(6 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…More so it makes both variance and covariance among the model parameter estimates small. However, Chasiotis et al [27,28] proved that two saturated ±1 designs of order 22, already existing in the current literature, are the D-optimal ones. They performed an exhaustive search for potential Gram matrices with determinant exceeding those of the provided designs, finding 25 such matrices.…”

Section: D-optimality Criterionmentioning

confidence: 99%

Exploration of D-, A-, I- and G- Optimality Criteria in Mixture Modeling

Wanyonyi

Okango

Koech

2021

AJPAS

View full text Add to dashboard Cite

A design optimality criterion, such as D-, A-, I-, and G- optimality criteria, is often used to analyze, evaluate and compare different designs options in mixture modeling test. A mixture test is an experiment where the descriptive variable and response rely only on the mixture's relative ratio in the mix but not its composition. The study geared toward exploring D-, A-, I-, and G- optimality criteria and their efficiency in determining an optimal split-plot design in mixture modeling within the presences of process variables. We evaluated and discussed in detail D-, A-, I-, and G- optimality criteria based on literature review. We also explored and examine why I- and D-optimal criteria are often involved within the formulation of an optimal design in the context of mixture process variable settings. We recommend that optimality criterion must always be used when assessing the various styles of designs so as to search out a desirable design that matches a combination model.

show abstract

Section: D-optimality Criterionmentioning

confidence: 99%

Exploration of D-, A-, I- and G- Optimality Criteria in Mixture Modeling

Wanyonyi

Okango

Koech

2021

AJPAS

View full text Add to dashboard Cite

show abstract

“…Recent work of Chasiotis, Kounias and Farmakis [9,10] addresses the smallest of these cases, n = 22. Having identified two matrices with large determinant, they perform an exhaustive search for potential Gram matrices with determinant exceeding those of their examples, finding 25 such matrices.…”

Section: A Refined Bound and The Case N ≡ 2 Modmentioning

confidence: 99%

“…Having identified two matrices with large determinant, they perform an exhaustive search for potential Gram matrices with determinant exceeding those of their examples, finding 25 such matrices. Each of these is excluded from being a Gram matrix, and thus the maximal determinant is established to be 40 • 20 10 , with two inequivalent Gram matrices being realisable. This should be compared to the bound 42•20 10 .…”

Section: A Refined Bound and The Case N ≡ 2 Modmentioning

confidence: 99%

“…Each of these is excluded from being a Gram matrix, and thus the maximal determinant is established to be 40 • 20 10 , with two inequivalent Gram matrices being realisable. This should be compared to the bound 42•20 10 . To our knowledge, the maximal determinant at any order greater than 22 satisfying n ≡ 2 mod 4 for which 2n − 2 is not a sum of two squares remains open.…”

Section: A Refined Bound and The Case N ≡ 2 Modmentioning

confidence: 99%

See 1 more Smart Citation

A Survey of the Hadamard Maximal Determinant Problem

Browne¹,

Egan²,

Hegarty³

et al. 2021

Preprint

View full text Add to dashboard Cite

In a celebrated paper of 1893, Hadamard established the maximal determinant theorem, which establishes an upper bound on the determinant of a matrix with complex entries of norm at most 1. His paper concludes with the suggestion that mathematicians study the maximum value of the determinant of an n × n matrix with entries in {±1}. This is the Hadamard maximal determinant problem.This survey provides complete proofs of the major results obtained thus far. We focus equally on upper bounds for the determinant (achieved largely via the study of the Gram matrices), and constructive lower bounds (achieved largely via quadratic residues in finite fields and concepts from design theory). To provide an impression of the historical development of the subject, we have attempted to modernise many of the original proofs, while maintaining the underlying ideas. Thus some of the proofs have the flavour of determinant theory, and some appear in print in English for the first time.We survey constructions of matrices in order n ≡ 3 mod 4, giving asymptotic analysis which has not previously appeared in the literature. We prove that there exists an infinite family of matrices achieving at least 0.48 of the maximal determinant bound. Previously the best known constant for a result of this type was 0.34. MSC: 05B20, 15B34

show abstract

“…Recent work of Chasiotis, Kounias and Farmakis [13] addresses the smallest of these cases, n = 22. Having identified two matrices with large determinant, they perform an exhaustive search for potential Gram matrices with determinant exceeding those of their examples, finding 25 such matrices.…”

Section: A Refined Bound and The Case N ≡ 2 Modmentioning

confidence: 99%

A Survey of the Hadamard Maximal Determinant Problem

Browne

Egan

Hegarty

et al. 2021

Electron. J. Combin.

View full text Add to dashboard Cite

In a celebrated paper of 1893, Hadamard established the maximal determinant theorem, which establishes an upper bound on the determinant of a matrix with complex entries of norm at most 1. His paper concludes with the suggestion that mathematicians study the maximum value of the determinant of an $n \times n$ matrix with entries in $\{ \pm 1\}$. This is the Hadamard maximal determinant problem. This survey provides complete proofs of the major results obtained thus far. We focus equally on upper bounds for the determinant (achieved largely via the study of the Gram matrices), and constructive lower bounds (achieved largely via quadratic residues in finite fields and concepts from design theory). To provide an impression of the historical development of the subject, we have attempted to modernise many of the original proofs, while maintaining the underlying ideas. Thus some of the proofs have the flavour of determinant theory, and some appear in print in English for the first time. We survey constructions of matrices in order $n \equiv 3 \mod 4$, giving asymptotic analysis which has not previously appeared in the literature. We prove that there exists an infinite family of matrices achieving at least 0.48 of the maximal determinant bound. Previously the best known constant for a result of this type was 0.34.

show abstract

The D-optimal saturated designs of order 22

Cited by 4 publications

References 13 publications

Exploration of D-, A-, I- and G- Optimality Criteria in Mixture Modeling

Exploration of D-, A-, I- and G- Optimality Criteria in Mixture Modeling

A Survey of the Hadamard Maximal Determinant Problem

A Survey of the Hadamard Maximal Determinant Problem

Contact Info

Product

Resources

About