Promenading in the enchanted realm of Kronecker powers: single monomial probabilistic evolution theory (PREVTH) in evolver dynamics

Demіralp, Metin

doi:10.1007/s10910-017-0822-0

Cited by 5 publications

(2 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Second degree multinomial functions may be formed from multinomial functions [20,21]. Single monomial functions may be formed from multinomial functions [19,25,26]: obtaining purely second degree multinomials from second degree multinomials is a special case of this. Putting it together, it is always possible to obtain purely second degree multinomial functions from multinomial functions.…”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Solving ODEs by Obtaining Purely Second Degree Multinomials via Branch and Bound with Admissible Heuristic

Gözükırmızı

Demіralp

2019

Mathematics

Self Cite

View full text Add to dashboard Cite

Probabilistic evolution theory (PREVTH) forms a framework for the solution of explicit ODEs. The purpose of the paper is two-fold: (1) conversion of multinomial right-hand sides of the ODEs to purely second degree multinomial right-hand sides by space extension; (2) decrease the computational burden of probabilistic evolution theory by using the condensed Kronecker product. A first order ODE set with multinomial right-hand side functions may be converted to a first order ODE set with purely second degree multinomial right-hand side functions at the expense of an increase in the number of equations and unknowns. Obtaining purely second degree multinomial right-hand side functions is important because the solution of such equation set may be approximated by probabilistic evolution theory. A recent article by the authors states that the ODE set with the smallest number of unknowns can be found by searching. This paper gives the details of a way to search for the optimal space extension. As for the second purpose of the paper, the computational burden can be reduced by considering the properties of the Kronecker product of vectors and how the Kronecker product appears within the recursion of PREVTH: as a Cauchy product structure.

show abstract

Section: Methodsmentioning

confidence: 99%

“…Squarification is facilitated by the recursion of squarification [9,17,18]. It is also possible to obtain single monomial right-hand side functions from multinomial right-hand side functions through space extension [19].…”

Section: Introductionmentioning

confidence: 99%

Solving ODEs by Obtaining Purely Second Degree Multinomials via Branch and Bound with Admissible Heuristic

Gözükırmızı

Demіralp

2019

Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

Using enchanted features of Constancy Adding Space Extension (CASE) to reduce the dimension of evolver dynamics: Single Monomial Probabilistic Evolution Theory

Özdemir

Demіralp

2018

J Math Chem

View full text Add to dashboard Cite

Pure quadratization and solution of ordinary differential equations by probabilistic evolution theory with concurrent computation of coefficients using exact arithmetic

Gözükırmızı

2023

J Math Chem

View full text Add to dashboard Cite

Promenading in the enchanted realm of Kronecker powers: single monomial probabilistic evolution theory (PREVTH) in evolver dynamics

Cited by 5 publications

References 21 publications

Solving ODEs by Obtaining Purely Second Degree Multinomials via Branch and Bound with Admissible Heuristic

Solving ODEs by Obtaining Purely Second Degree Multinomials via Branch and Bound with Admissible Heuristic

Using enchanted features of Constancy Adding Space Extension (CASE) to reduce the dimension of evolver dynamics: Single Monomial Probabilistic Evolution Theory

Pure quadratization and solution of ordinary differential equations by probabilistic evolution theory with concurrent computation of coefficients using exact arithmetic

Contact Info

Product

Resources

About