Infinite Systems of Linear Equations
Infinite systems of linear equations are usually 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. The talk will
present the early history and recent important achievements.
Unexpected examples and computational experiments will motivate and
illustrate the main results. Special attention will be paid to the
case of Toeplitz matrices with continuous and discontinuous
symbols.
