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Iterative methods (Mathematics) --- Algorithms --- Equations

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This book focuses on iterative methods for solving the Cauchy problem associated with the Helmholtz equation, a significant inverse problem in acoustics and field measurements. It explores how to recover solutions in a domain when only partial boundary data is available. The work addresses the ill-posed nature of the problem, where small errors in data can lead to large errors in solutions. By introducing modifications such as an artificial interior boundary and using conjugate gradient type methods, the author Lydie Mpinganzima develops techniques to restore stability and improve convergence speed. The book is intended for mathematicians and engineers interested in numerical methods for partial differential equations, particularly the Helmholtz equation.

Iterative methods (Mathematics) --- Helmholtz equation.

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This thesis focuses on the iterative procedures for addressing the Cauchy problem for elliptic equations, particularly in unbounded domains. It examines the challenges of solving ill-posed problems, which are prevalent in various scientific and engineering applications. The work builds on methods initially proposed for the Laplace equation and extends them to the Helmholtz equation. The study demonstrates the convergence of iterative methods under specific conditions, emphasizing the importance of parameter choice in the Robin condition. It also explores the application of these methods in numerical experiments, highlighting their potential in fields like medicine and acoustics. The thesis is aimed at researchers and students in applied mathematics and engineering.

Cauchy problem. --- Iterative methods (Mathematics)

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Algorithms. --- Versification. --- Iterative methods (Mathematics)

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Iterative methods (Mathematics) --- Itération (mathématiques)