Ebook: Topics in Numerical Analysis: With Special Emphasis on Nonlinear Problems

This volume contains eighteen papers submitted in celebration of the sixty-fifth birthday of Professor Tetsuro Yamamoto of Ehime University. Professor Yamamoto was born in Tottori, Japan on January 4, 1937. He obtained his B. S. and M. S. in mathematics from Hiroshima University in 1959 and 1961, respec­ tively. In 1966, he took a lecturer position in the Department of Mathematics, Faculty of General Education, Hiroshima University and obtained his Ph. D. degree from Hiroshima University two years later. In 1969, he moved to the Department of Applied Mathematics, Faculty of Engineering, Ehime University as an associate professor and he has been a full professor of the Department of Mathematics (now Department of Mathematical Sciences), Faculty of Science, since 1975. At the early stage of his study, he was interested in algebraic eigen­ value problems and linear iterative methods. He published some papers on these topics in high level international journals. After moving to Ehime University, he started his research on Newton's method and Newton-like methods for nonlinear operator equations. He published many papers on error estimates of the methods. He established the remarkable result that all the known error bounds for Newton's method under the Kantorovich assumptions follow from the Newton-Kantorovich theorem, which put a period to the race of finding sharper error bounds for Newton's method.

---

This collection of papers on numerical analysis with special emphasis on nonlinear problems covers a broad spectrum of fields. Several papers are involved in applying numerical methods for proving the existence of solutions of nonlinear problems, e.g. of boundary problems or of obstacle problems. Naturally the solution of linear and nonlinear problems by iterative methods is the subject of a couple of papers. Here topics like the fast verification of solutions of monotone matrix equations, the convergence of linear asynchronous iteration with spectral radius of modulus one or aggregation and disaggregation methods for p-cyclic Markov chains are treated. On the other hand papers involved in optimization problems can be found. Nearly all fields of modern numerical analysis are touched by at least one paper.

---

This collection of papers on numerical analysis with special emphasis on nonlinear problems covers a broad spectrum of fields. Several papers are involved in applying numerical methods for proving the existence of solutions of nonlinear problems, e.g. of boundary problems or of obstacle problems. Naturally the solution of linear and nonlinear problems by iterative methods is the subject of a couple of papers. Here topics like the fast verification of solutions of monotone matrix equations, the convergence of linear asynchronous iteration with spectral radius of modulus one or aggregation and disaggregation methods for p-cyclic Markov chains are treated. On the other hand papers involved in optimization problems can be found. Nearly all fields of modern numerical analysis are touched by at least one paper.
Content:
Front Matter....Pages I-XII
A Unified Approach for Bounding the Positive Root of Certain Classes of Polynomials with Applications....Pages 1-7
Numerical Verifications of Solutions for Obstacle Problems....Pages 9-19
On the Existence Theorems of Kantorovich, Moore and Miranda....Pages 21-28
A Survey of Robust Preconditioning Methods....Pages 29-48
A Box-Constrained Optimization Algorithm with Negative Curvature Directions and Spectral Projected Gradients....Pages 49-60
Inclusions and Existence Proofs for Solutions of a Nonlinear Boundary Value Problem by Spectral Numerical Methods....Pages 61-77
A Superlinearly and Globally Convergent Method for Reaction and Diffusion Problems with a Non-Lipschitzian Operator....Pages 79-90
On Linear Asynchronous Iterations when the Spectral Radius of the Modulus Matrix is One....Pages 91-104
Iterative Methods for Eigenvalue Problems with Nondifferentiable Normalized Condition of a General Complex Matrix....Pages 105-118
Global Optimization in Quadratic Semi-Infinite Programming....Pages 119-132
Aggregation/Disaggregation Methods for p-cyclic Markov Chains....Pages 133-150
A New Way to Describe the Symmetric Solution Set Ssym of Linear Interval Systems....Pages 151-163
A Guaranteed Bound of the Optimal Constant in the Error Estimates for Linear Triangular Element....Pages 165-173
Fast Verification of Solutions for Sparse Monotone Matrix Equations....Pages 175-187
Laguerre-like Methods for the Simultaneous Approximation of Polynomial Zeros....Pages 189-209
A Smoothing Newton Method for Ball Constrained Variational Inequalities with Applications....Pages 211-225
An Explicit Inversion Formula for Tridiagonal Matrices....Pages 227-238
On the Rate of Convergence of the Levenberg-Marquardt Method....Pages 239-249

---

This collection of papers on numerical analysis with special emphasis on nonlinear problems covers a broad spectrum of fields. Several papers are involved in applying numerical methods for proving the existence of solutions of nonlinear problems, e.g. of boundary problems or of obstacle problems. Naturally the solution of linear and nonlinear problems by iterative methods is the subject of a couple of papers. Here topics like the fast verification of solutions of monotone matrix equations, the convergence of linear asynchronous iteration with spectral radius of modulus one or aggregation and disaggregation methods for p-cyclic Markov chains are treated. On the other hand papers involved in optimization problems can be found. Nearly all fields of modern numerical analysis are touched by at least one paper.
Content:
Front Matter....Pages I-XII
A Unified Approach for Bounding the Positive Root of Certain Classes of Polynomials with Applications....Pages 1-7
Numerical Verifications of Solutions for Obstacle Problems....Pages 9-19
On the Existence Theorems of Kantorovich, Moore and Miranda....Pages 21-28
A Survey of Robust Preconditioning Methods....Pages 29-48
A Box-Constrained Optimization Algorithm with Negative Curvature Directions and Spectral Projected Gradients....Pages 49-60
Inclusions and Existence Proofs for Solutions of a Nonlinear Boundary Value Problem by Spectral Numerical Methods....Pages 61-77
A Superlinearly and Globally Convergent Method for Reaction and Diffusion Problems with a Non-Lipschitzian Operator....Pages 79-90
On Linear Asynchronous Iterations when the Spectral Radius of the Modulus Matrix is One....Pages 91-104
Iterative Methods for Eigenvalue Problems with Nondifferentiable Normalized Condition of a General Complex Matrix....Pages 105-118
Global Optimization in Quadratic Semi-Infinite Programming....Pages 119-132
Aggregation/Disaggregation Methods for p-cyclic Markov Chains....Pages 133-150
A New Way to Describe the Symmetric Solution Set Ssym of Linear Interval Systems....Pages 151-163
A Guaranteed Bound of the Optimal Constant in the Error Estimates for Linear Triangular Element....Pages 165-173
Fast Verification of Solutions for Sparse Monotone Matrix Equations....Pages 175-187
Laguerre-like Methods for the Simultaneous Approximation of Polynomial Zeros....Pages 189-209
A Smoothing Newton Method for Ball Constrained Variational Inequalities with Applications....Pages 211-225
An Explicit Inversion Formula for Tridiagonal Matrices....Pages 227-238
On the Rate of Convergence of the Levenberg-Marquardt Method....Pages 239-249
....