Solution of Kronecker Product Initial Value Problems Associated with First Order Difference System via Tensor— based Hardness of the Shortest Vector Problem

• Дата: 2008
• Автори: Murty, K.N., Balaram, V.V.S.S.S., Viswanadh, K.
• Формат: Стаття
• Мова: English
• Опубліковано: Інститут проблем моделювання в енергетиці ім. Г.Є. Пухова НАН України 2008
• Назва видання: Электронное моделирование
• Теми: Математические методы и модели
• Онлайн доступ: http://dspace.nbuv.gov.ua/handle/123456789/101603
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: Solution of Kronecker Product Initial Value Problems Associated with First Order Difference System via Tensor— based Hardness of the Shortest Vector Problem / K.N. Murty, V.V.S.S.S. Balaram, K. Viswanadh // Электронное моделирование. — 2008. — Т. 30, № 6. — С. 19-33. — Бібліогр.: 10 назв. — англ.

This paper presents criteria for the existence and uniqueness of solution to Kronecker product initial value problem associated with general first order matrix difference system. A modified least square method and a modified QR algorithm are developed to find the best least square solution of the Kronecker product of matrices. Using these methods as a tool the general solution of the Kronecker product initial value problem whose initial condition matrix is over determined is established. Using the method developed by Ishey Haviv and Îded Regev, on finding shortest vector problem we improve further the best least square solution. To boost the hardness factor we simply apply the standard Kronecker product or tensor product of lattices.