An inverse problem for Toeplitz matrices

Approximate inverse-free preconditioners for Toeplitz matrices

In this paper, we propose approximate inverse-free preconditioners for solving Toeplitz systems. The preconditioners are constructed based on the famous Gohberg-Sememcul formula. We show that if a Toepltiz matrix is generated by a positive bounded function and its entries enjoys the off-diagonal decay property, then the eigenvalues of the preconditioned matrix are clustered around one. Experime...

On group inverse of singular Toeplitz matrices

In this paper we show that the group inverse of a real singular Toeplitz matrix can be represented as the sum of products of lower and upper triangular Toeplitz matrices. Such a matrix representation generalizes “Gohberg–Semencul formula” in the literature. © 2004 Elsevier Inc. All rights reserved. AMS classification: 15A09; 65F20

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

Numerical Solution of the Inverse Eigenvalue Problem for Real Symmetric Toeplitz Matrices

Some remarks on the inverse eigenvalue problem for real symmetric Toeplitz matrices

Two theorems about the solution properties of the Toeplitz Inverse Eigenvalue Problem (ToIEP) are introduced and proved. One of them is applied to make a better starting generator and the other can be used to double the number of solutions found. These applications are tested through a short Mathematica program. Also an optimisation method for solving ToIEP with global convergence property is p...