The paper by Jorge J. More and D. C. Sorensen presents an algorithm for solving the problem of minimizing a quadratic function subject to an ellipsoidal constraint, which is guaranteed to produce a nearly optimal solution in a finite number of iterations. This algorithm is crucial for computing the step between iterates in trust region methods for optimization problems. The authors also explore the use of their algorithm in a trust region Newton's method, proving that under reasonable assumptions, the sequence generated by Newton's method converges to a point satisfying the first and second-order necessary conditions for a minimizer of the objective function. Numerical results for GQTPAR, a Fortran implementation of their algorithm, show that it is highly effective in trust region methods, with an average of 1.6 iterations per call. The paper discusses the theoretical basis of the algorithm, its implementation, and its performance in various test cases, demonstrating its robustness and efficiency.The paper by Jorge J. More and D. C. Sorensen presents an algorithm for solving the problem of minimizing a quadratic function subject to an ellipsoidal constraint, which is guaranteed to produce a nearly optimal solution in a finite number of iterations. This algorithm is crucial for computing the step between iterates in trust region methods for optimization problems. The authors also explore the use of their algorithm in a trust region Newton's method, proving that under reasonable assumptions, the sequence generated by Newton's method converges to a point satisfying the first and second-order necessary conditions for a minimizer of the objective function. Numerical results for GQTPAR, a Fortran implementation of their algorithm, show that it is highly effective in trust region methods, with an average of 1.6 iterations per call. The paper discusses the theoretical basis of the algorithm, its implementation, and its performance in various test cases, demonstrating its robustness and efficiency.