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Improve EM simulation efforts fast with this applications-focused resource. This unique volume is the first book on integral equation-based methods that combines quantitative formulas for predicting numerical simulation accuracy together with rigorous error estimates and results for dozens of actual electromagnetics and wave propagation problems. You get the latest insights on accuracy-improving methods like regularization and error-increasing effects such as edge singularities and resonance, along with full details on how to determine mesh density, choice of basis functions, and other parameters needed to optimize any numerical simulation. Bridging the gap between abstract academic treatments and the real-world needs of engineers, this timely work introduces various surface integral equation formulations, approaches to discretizing the integral equations, and measures of solution accuracy. It gives you numerical methods for 2D radiation and scattering problems, emphasizing concrete solution error bounds with exactly given constants. Moreover, the book provides techniques for higher order basis functions and 3D problems, focusing on smooth scatterers and edge singularity effects. This informative reference also explores problems involving resonant cavities and structures, and features a comprehensive treatment of resonant scatterers. The final chapter covers the convergence of the fast multipole method with iterative linear system solvers, complete with practical methods for improving the efficiency of iterative solutions.

Electromagnetism --- Error analysis (Mathematics) --- Errors, Theory of --- Instrumental variables (Statistics) --- Mathematical statistics --- Numerical analysis --- Statistics --- Mathematics.

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If you are working in digital signal processing, control or numerical analysis, you will find this authoritative analysis of quantization noise (roundoff error) invaluable. Do you know where the theory of quantization noise comes from, and under what circumstances it is true? Get answers to these and other important practical questions from expert authors, including the founder of the field and formulator of the theory of quantization noise, Bernard Widrow. The authors describe and analyze uniform quantization, floating-point quantization, and their applications in detail. Key features include: • Analysis of floating point round off • Dither techniques and implementation issues analyzed • Offers heuristic explanations along with rigorous proofs, making it easy to understand 'why' before the mathematical proof is given.

Roundoff errors. --- Roundoff errors --- Error analysis (Mathematics) --- Numerical analysis --- Errors, Theory of --- Instrumental variables (Statistics) --- Mathematical statistics --- Statistics

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This volume provides a posteriori error analysis for mathematical idealizations in modeling boundary value problems, especially those arising in mechanical applications, and for numerical approximations of numerous nonlinear variational problems. The author avoids giving the results in the most general, abstract form so that it is easier for the reader to understand more clearly the essential ideas involved. Many examples are included to show the usefulness of the derived error estimates. Audience This volume is suitable for researchers and graduate students in applied and computational mathematics, and in engineering.

Error analysis (Mathematics) --- Duality theory (Mathematics) --- Algebra --- Mathematical analysis --- Topology --- Errors, Theory of --- Instrumental variables (Statistics) --- Mathematical statistics --- Numerical analysis --- Statistics

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Error analysis (Mathematics) --- #SBIB:303H510 --- Methoden sociale wetenschappen: statistische technieken, algemeen --- Error analysis (Mathematics). --- Errors, Theory of --- Instrumental variables (Statistics) --- Mathematical statistics --- Numerical analysis --- Statistics

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Error analysis (Mathematics) --- Regression analysis --- Analysis, Regression --- Linear regression --- Regression modeling --- Errors, Theory of --- Mathematical statistics --- Multivariate analysis --- Structural equation modeling --- Instrumental variables (Statistics) --- Numerical analysis --- Statistics