- Published Year: 2008
- Page count: 515
- File Size: 3 Mb
- Language: English
- Published by: The Johns Hopkins University Press
- Visited by: 2
- Rating/Review: 4.3
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ISBN:
0801890527
9780801890529
Keywords:
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Learn MoreMatrix Computations and Semiseparable Matrices: Eigenvalue and Singular Value Methods (Volume 2)
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Each download or ask from book AI costs 2 points. To earn more free points, please visit the Points Guide Page and complete some valuable actions.Introduction to "Matrix Computations and Semiseparable Matrices: Eigenvalue and Singular Value Methods (Volume 2)"
Written by Raf Vandebril, Marc Van Barel, and Nicola Mastronardi, this book delves into the computational methods and techniques pivotal to understanding semiseparable matrices and the corresponding eigenvalue and singular value problems. This second volume in the series provides an advanced analysis, offering a clear and structured treatment of matrix computations, particularly for researchers, practitioners, and graduate students in numerical linear algebra.
Highly regarded for bridging the theoretical concepts and practical applications of linear algebra, this book covers cutting-edge methods and algorithms associated with eigenvalue and singular value computations for semiseparable matrices. By incorporating computational efficiency, it provides both a theoretical foundation and real-world implications, ensuring a comprehensive resource for advanced matrix analysis.
Detailed Summary of the Book
Divided into meticulously crafted chapters, the book focuses on matrix computations related to semiseparable matrices, specifically addressing eigenvalue and singular value problems. Semiseparable matrices—critical in modern numerical methods—are structured matrices that arise naturally in various applications such as signal processing, systems theory, and computational science.
The book systematically explains:
- Theoretical underpinnings of eigenvalue and singular value computations.
- Numerically stable and computationally efficient algorithms for semiseparable structures.
- Techniques to exploit semiseparable properties for faster computation of matrix decompositions.
- Applications of these advanced methodologies in practical scenarios.
By leveraging modern computational techniques, the authors strive to enable engineers, mathematicians, and scientists to tackle complex matrix problems with an optimal approach. Unlike traditional methods, the novel approaches discussed in this book emphasize computational speed without sacrificing accuracy, making it a timeless addition to numerical linear algebra literature.
Key Takeaways
This book provides a unique lens to explore semiseparable matrices, offering insights that benefit both academia and industry. Some of the key takeaways include:
- A comprehensive understanding of eigenvalue and singular value decomposition for semiseparable matrices.
- The development of fast numerical algorithms tailored to structured matrices.
- Advanced insights into minimizing computational complexity without impacting solution precision.
- Applicable methods for real-world problems in engineering, physics, and data science.
- A harmonious blend of theory and computational practice, ensuring strong foundational knowledge coupled with actionable techniques.
Famous Quotes from the Book
"Matrix computations are the cornerstone of numerical mathematics; they embody the perfect union of structure, theory, and applications."
"The development of specialized algorithms for structured matrices paves the way for revolutionary advancements in computation, where precision meets efficiency."
"Understanding semiseparable matrices means unlocking the hidden potential of matrix computations; a journey where complexity meets elegance."
Why This Book Matters
As modern applications demand faster, more efficient computation methods, structured matrices such as semiseparable ones offer a promising solution. This book contributes significantly to the field by addressing eigenvalue and singular value computations—a core area in numerical analysis—and presenting methods uniquely tailored to semiseparable structures.
Its importance lies in its ability to bridge the ever-increasing gap between theoretical advancements and practical implementation. This work equips researchers and professionals alike with the tools and insights to solve large-scale computational problems while honoring the intricacies of structured data.
Moreover, the emphasis on semiseparable matrices reflects their growing relevance in computational science and beyond—making this book an essential guide for anyone looking to specialize in structured matrix theory and computation. Whether you're a seasoned expert or a passionate learner, this volume expands your horizons and deepens your understanding of the field.
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