Infinite systems of linear equations
by
Israel Gohberg
Tel Aviv University

Solving infinite systems of linear equations is an important problem of operator theory; usually the systems are solved by the method of finite sections. This means that the infinite system is replaced by the sequence of finite sections of the original system and it is expected that the solutions of the finite systems converge to the solution of the infinite system. This method has a rich history of 150 years and many distinguished mathematicians have made important contributions in this area which will be reviewed. Unexpected examples and computational experiments will motivate and illustrate the main results. Special attention will be paid to the case of Toeplitz matrices with discontinuous symbols.

Date received: June 24, 2002