Solutions to Problems Posed in Volume 20(1) and 20(2): 04.2.1. A  Range Equality for Block Matrices with Orthogonal Projectors—Solution

AbstractWe present the conditions for a block matrix of a ring to have the image-kernel{(p,q)}-inverse in the generalized Banachiewicz–Schur form. We give representations for the image-kernel inverses of the sum and the product of two block matrices. Some characterizations of the image-kernel{(p,q)}-inverse in a ring with involution are investigated too.

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Algorithms for solving scattering problems for the Manakov model of nonlinear Schrödinger equations

Journal of Inverse and Ill-Posed Problems ◽

10.1515/jiip-2020-0126 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Leonid L. Frumin

Keyword(s):

Scattering Problem ◽

Inverse Scattering Problem ◽

Numerical Algorithms ◽

Scattering Problems ◽

Block Matrices ◽

Nonlinear Schrödinger ◽

Direct Scattering ◽

Vector Case ◽

Manakov Model ◽

Vector Variant

AbstractWe introduce numerical algorithms for solving the inverse and direct scattering problems for the Manakov model of vector nonlinear Schrödinger equation. We have found an algebraic group of 4-block matrices with off-diagonal blocks consisting of special vector-like matrices for generalizing the scalar problem’s efficient numerical algorithms to the vector case. The inversion of block matrices of the discretized system of Gelfand–Levitan–Marchenko integral equations solves the inverse scattering problem using the vector variant the Toeplitz Inner Bordering algorithm of Levinson’s type. The reversal of steps of the inverse problem algorithm gives the solution of the direct scattering problem. Numerical tests confirm the proposed vector algorithms’ efficiency and stability. We also present an example of the algorithms’ application to simulate the Manakov vector solitons’ collision.

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Euclidean norm estimates of the inverse of some special block matrices

Applied Mathematics and Computation ◽

10.1016/j.amc.2016.02.048 ◽

2016 ◽

Vol 284 ◽

pp. 12-23 ◽

Cited By ~ 1

Author(s):

Ljiljana Cvetković ◽

Vladimir Kostić ◽

Ksenija Doroslovački ◽

Dragana Lj. Cvetković

Keyword(s):

Euclidean Norm ◽

Block Matrices ◽

Norm Estimates

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Perturbations of Fredholm linear relations in Banach spaces with application to 3×3-block matrices of linear relations

Arab Journal of Mathematical Sciences ◽

10.1016/j.ajmsc.2015.05.001 ◽

2016 ◽

Vol 22 (1) ◽

pp. 59-76 ◽

Cited By ~ 4

Author(s):

Aymen Ammar ◽

Toka Diagana ◽

Aref Jeribi

Keyword(s):

Banach Spaces ◽

Block Matrices ◽

Linear Relations

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Structure of positive block-matrices and nonstationary prediction

Journal of Functional Analysis ◽

10.1016/0022-1236(87)90119-4 ◽

1987 ◽

Vol 70 (2) ◽

pp. 402-425 ◽

Cited By ~ 5

Author(s):

Gr Arsene ◽

T Constantinescu

Keyword(s):

Block Matrices

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Neutrosophic Soft Block Matrices And Some Of Its Properties

10.54216/ijns.120105 ◽

2020 ◽

pp. 39-49

Author(s):

admin admin ◽

Keyword(s):

Decision Making ◽

Crucial Role ◽

Real Life ◽

Decision Making Process ◽

Mathematical Tool ◽

Soft Sets ◽

Neutrosophic Sets ◽

Block Matrices ◽

Inconsistent Information

In real life situations, there are many issues in which there are uncertainties, vagueness, complexities and unpredictability. Neutrosophic sets are a mathematical tool to address some issues which cannot be met using the existing methods. Neutrosophic soft matrices play a crucial role in handling indeterminant and inconsistent information during decision making process. The main focus of this article is to discuss the concept of neutrosophic sets, neutrosophic soft sets, neutrosophic soft matrices theory and finally to discuss about neutrosophic soft block matrics which are very useful and applicable in various situations involving uncertainties and imprecisions. In this article, neutrosophic soft block matrices, various types of neutrosophic soft block matrices, some operations on it along with some properties associated with it are discussed in details.

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