# 42539

## Автор(ов):

2

Параметры публикации

Тезисы доклада

## Название:

Norm variability in Newton method for underdetermined systems of equations

## Наименование конференции:

• 17th Baikal international school-seminar "Methods of Optimization and Their Applications" (Иркутск, 2017)

## Наименование источника:

• Abstracts of the 17th Baikal international school-seminar "Methods of Optimization and Their Applications" (Иркутск, 2017)

• Иркутск

• ESI SB RAS

2017

## Страницы:

57-57
Аннотация
Newton method may serve as a tool for solution of underdetermined systems of algebraic (differentiable) equations P(x) = 0, P : Rn -> Rm , m < n. It is usually written via pseudo-inverse matrix, which correspond to Euclidean norms in pre-image and image spaces [1, 4]. The same method can be used to explore image set of a non-linear differentiable mapping g(x) , resulting in equations of type g(x) = c y, with chosen direction y. We propose variable-norm setup for Newton method. Using generic convergence conditions, based on technique of [2, 3] we study different norm combinations, choice of norms for image exploration problems, as well as constant estimation issues related with norm choice.

## Библиографическая ссылка:

Поляк Б.Т., Тремба А.А. Norm variability in Newton method for underdetermined systems of equations / Abstracts of the 17th Baikal international school-seminar "Methods of Optimization and Their Applications" (Иркутск, 2017). Иркутск: ESI SB RAS, 2017. С. 57-57.