Accurate polynomial root-finding methods for symmetric tridiagonal matrix eigenproblems

作者：Gemignani L^*

来源：Computers & Mathematics with Applications, 2016, 72(4): 992-1001.

DOI：10.1016/j.camwa.2016.06.009

• Polynomial zeros
• Tridiagonal matrix
• Matrix eigenvalues
• Three-term recurrence
• Floating-point arithmetic
• Accuracy

In this paper we consider the application of polynomial root-finding methods to the solution of the tridiagonal matrix eigenproblem. All considered solvers are based on evaluating the Newton correction. We show that the use of scaled three-term recurrence relations complemented with error free transformations yields some compensated schemes which significantly improve the accuracy of computed results at a modest increase in computational cost. Numerical experiments illustrate that under some restriction on the conditioning the novel iterations can approximate and/or refine the eigenvalues of a tridiagonal matrix with high relative accuracy.

• 出版日期2016-8