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# Numerical Approximation of the Product of the Square Root of a Matrix With a Vector

@inproceedings{Allen2005NumericalAO, title={Numerical Approximation of the Product of the Square Root of a Matrix With a Vector}, author={Edward J. Allen and James Baglama and Steven K. Boyd}, year={2005} }

- Published 2005

Given an n × n symmetric positive definite matrix A and a vector ~c, two numerical methods for approximating A1/2~c are developed, analyzed, and computationally tested. The first method applies a Newton iteration to a specific nonlinear system to approximate A1/2~c while the second method applies a step-control method to numerically solve a specific initial-value problem to approximate A1/2~c. Assuming that A is first reduced to tridiagonal form, the first method requires O(n2) operations per… CONTINUE READING