A Journey Through The History Of Numerical Linear Algebra

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A Journey Through The History Of Numerical Linear Algebra

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Author : Claude Brezinski
language : en
Publisher: SIAM
Release Date : 2022-12-06

A Journey Through The History Of Numerical Linear Algebra written by Claude Brezinski and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-06 with Mathematics categories.

This expansive volume describes the history of numerical methods proposed for solving linear algebra problems, from antiquity to the present day. The authors focus on methods for linear systems of equations and eigenvalue problems and describe the interplay between numerical methods and the computing tools available at the time. The second part of the book consists of 78 biographies of important contributors to the field. A Journey through the History of Numerical Linear Algebra will be of special interest to applied mathematicians, especially researchers in numerical linear algebra, people involved in scientific computing, and historians of mathematics.

Hessenberg And Tridiagonal Matrices

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Author : Gérard Meurant
language : en
Publisher: SIAM
Release Date : 2025-06-10

Hessenberg And Tridiagonal Matrices written by Gérard Meurant and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-10 with Mathematics categories.

This is the only book devoted exclusively to Hessenberg and tridiagonal matrices. Hessenberg matrices are involved in Krylov methods for solving linear systems or computing eigenvalues and eigenvectors, in the QR algorithm for computing eigenvalues, and in many other areas of scientific computing (for instance, control theory). Matrices that are both upper and lower Hessenberg are tridiagonal. Their entries are zero except for the main diagonal and the subdiagonal and updiagonal next to it. Hessenberg and Tridiagonal Matrices: Theory and Examples presents known and new results; describes the theoretical properties of the matrices, their determinants, LU factorizations, inverses, and eigenvalues; illustrates the theoretical properties with applications and examples as well as numerical experiments; and considers unitary Hessenberg matrices, inverse eigenvalue problems, and Toeplitz tridiagonal matrices. This book is intended for applied mathematicians, especially those interested in numerical linear algebra, and it will also be of interest to physicists and engineers.

Error Norm Estimation In The Conjugate Gradient Algorithm

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Author : Gérard Meurant
language : en
Publisher: SIAM
Release Date : 2024-01-30

Error Norm Estimation In The Conjugate Gradient Algorithm written by Gérard Meurant and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-30 with Mathematics categories.

The conjugate gradient (CG) algorithm is almost always the iterative method of choice for solving linear systems with symmetric positive definite matrices. This book describes and analyzes techniques based on Gauss quadrature rules to cheaply compute bounds on norms of the error. The techniques can be used to derive reliable stopping criteria. How to compute estimates of the smallest and largest eigenvalues during CG iterations is also shown. The algorithms are illustrated by many numerical experiments, and they can be easily incorporated into existing CG codes. The book is intended for those in academia and industry who use the conjugate gradient algorithm, including the many branches of science and engineering in which symmetric linear systems have to be solved.

Linear Perspectives A Journey Through Vector Spaces

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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-07-13

Linear Perspectives A Journey Through Vector Spaces written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-13 with Mathematics categories.

Embark on a transformative journey into the world of linear algebra with "Linear Perspectives: A Journey Through Vector Spaces", a comprehensive guide that unveils the elegance and power of this fundamental mathematical discipline. Written with clarity and accessibility, this book invites readers of all backgrounds to explore the captivating world of vectors, matrices, and linear transformations. Discover the essence of vector spaces, the underlying structures that govern the behavior of vectors. Delve into linear combinations, subspaces, linear independence, and dimension, gaining a deep understanding of the fundamental building blocks of linear algebra. Unravel the mysteries of linear transformations, powerful mathematical tools that map vectors from one space to another. Explore the concept of invertibility, unlocking the conditions under which a linear transformation can be reversed. Witness the elegance of matrix representations, providing a concise and efficient way to manipulate and analyze linear transformations. Journey into the realm of inner product spaces, a special class of vector spaces where vectors can be measured and compared using an inner product. Discover the beauty of orthogonality, projections, and the Gram-Schmidt process, unlocking new insights into solving systems of linear equations and understanding the geometry of vector spaces. Encounter eigenvalues and eigenvectors, two fundamental concepts that reveal the secrets of linear operators. Learn how eigenvalues and eigenvectors can be used to diagonalize matrices, transforming them into a simpler and more easily understandable form. Delve into the profound implications of the spectral theorem, a cornerstone of linear algebra that provides a deep and insightful understanding of linear operators. Explore the diverse applications of linear algebra across a wide range of disciplines, from computer graphics and machine learning to quantum mechanics, economics, and signal processing. Witness the remarkable versatility of linear algebra as it empowers researchers and practitioners to solve complex problems and gain new insights into the world around us. "Linear Perspectives: A Journey Through Vector Spaces" is an essential resource for students, researchers, and professionals seeking a comprehensive and engaging introduction to linear algebra. With its clear explanations, insightful examples, and thought-provoking exercises, this book will transform your understanding of this fundamental mathematical discipline and open up new avenues of exploration and discovery. If you like this book, write a review!

Applied Numerical Linear Algebra

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Author : James W. Demmel
language : en
Publisher: SIAM
Release Date : 1997-08-01

Applied Numerical Linear Algebra written by James W. Demmel and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-08-01 with Mathematics categories.

This comprehensive textbook is designed for first-year graduate students from a variety of engineering and scientific disciplines.

Mathemagics A Magical Journey Through Advanced Mathematics Connecting More Than 60 Magic Tricks To High Level Math

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Author : Ricardo V Teixeira
language : en
Publisher: World Scientific
Release Date : 2020-05-29

Mathemagics A Magical Journey Through Advanced Mathematics Connecting More Than 60 Magic Tricks To High Level Math written by Ricardo V Teixeira and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-29 with Mathematics categories.

'This delightful book connects mathematical concepts in a dozen areas to magic tricks. Expositions of the mathematics precede description and analysis of the tricks. The expositions are too short for in-depth learning; the intent is to give sophomores a taste of the content and ideas of later mathematics courses. Each chapter features exercises on the mathematics, and students can have fun practicing the tricks.'Mathematics MagazineTeixeira and Park present over 60 different magic tricks while introducing students to high-level math areas. Readers will learn really interesting ideas that will better prepare them for future courses and help them finding areas they might want to study deeper. And as a 'side effect' students will learn amazing magic tricks, century-old secrets, and details from famous magicians and mathematicians.The material was written to quickly present key concepts in several mathematical areas in direct way. Little or no proficiency in math is assumed. In fact, students do not require any Calculus knowledge. And since chapters are almost independent from each other, this book also work as introduction to several other courses.Topics covered include mathematical proofs, probability, abstract algebra, linear algebra, mathematical computing, number theory, coding theory, geometry, topology, real analysis, numerical analysis and history of math.

Numerical Linear Algebra

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Author : William Layton
language : en
Publisher: World Scientific
Release Date : 2020-07-14

Numerical Linear Algebra written by William Layton and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-14 with Mathematics categories.

'The numerical algorithms presented are written in pseudocode and based on MATLAB, a programming and numeric computing platform widely used in STEM fields. Thus, no formal training in computer science or knowledge of any specific programming language is needed to parse the algorithms. Summing up: Recommended.'CHOICEMany students come to numerical linear algebra from science and engineering seeking modern tools and an understanding of how the tools work and their limitations. Often their backgrounds and experience are extensive in applications of numerical methods but limited in abstract mathematics and matrix theory. Often enough it is limited to multivariable calculus, basic differential equations and methods of applied mathematics. This book introduces modern tools of numerical linear algebra based on this background, heavy in applied analysis but light in matrix canonical forms and their algebraic properties. Each topic is presented as algorithmic ideas and through a foundation based on mostly applied analysis. By picking a path through the book appropriate for the level, it has been used for both senior level undergraduates and beginning graduate classes with students from diverse fields and backgrounds.

Numerical Analysis Historical Developments In The 20th Century

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Author : C. Brezinski
language : en
Publisher: Elsevier
Release Date : 2012-12-02

Numerical Analysis Historical Developments In The 20th Century written by C. Brezinski and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Mathematics categories.

Numerical analysis has witnessed many significant developments in the 20th century. This book brings together 16 papers dealing with historical developments, survey papers and papers on recent trends in selected areas of numerical analysis, such as: approximation and interpolation, solution of linear systems and eigenvalue problems, iterative methods, quadrature rules, solution of ordinary-, partial- and integral equations. The papers are reprinted from the 7-volume project of the Journal of Computational and Applied Mathematics on '/homepage/sac/cam/na2000/index.htmlNumerical Analysis 2000'. An introductory survey paper deals with the history of the first courses on numerical analysis in several countries and with the landmarks in the development of important algorithms and concepts in the field.

The Search For Certainty

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Author : Frank J. Swetz
language : en
Publisher: Courier Corporation
Release Date : 2012-01-01

The Search For Certainty written by Frank J. Swetz and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-01 with Mathematics categories.

Self-contained and authoritative, this history of mathematics is suited to those with no math background. Its absorbing, entertaining essays focus on the era from 1800 to 2000. Contributors include Henri Poincaré, Judith V. Grabiner, and H. S. M. Coxeter, who discuss topics ranging from logic and infinity to Fermat's Last Theorem.

Mastering Linear Algebra

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Author : Cybellium
language : en
Publisher: Cybellium Ltd
Release Date :

Mastering Linear Algebra written by Cybellium and has been published by Cybellium Ltd this book supported file pdf, txt, epub, kindle and other format this book has been release on with Computers categories.

Unlock the Language of Vectors and Matrices for Enhanced Problem Solving In the realm of mathematics and science, linear algebra stands as a powerful language that underlies numerous disciplines. "Mastering Linear Algebra" is your definitive guide to understanding and harnessing the potential of this essential mathematical framework, empowering you to solve complex problems with clarity and precision. About the Book: As mathematical concepts become more integral to various fields, a strong grasp of linear algebra becomes increasingly valuable. "Mastering Linear Algebra" offers a comprehensive exploration of this foundational subject—a cornerstone of mathematics and its applications. This book caters to both newcomers and experienced learners aiming to excel in linear algebra concepts, computations, and applications. Key Features: Linear Algebra Fundamentals: Begin by understanding the core principles of linear algebra. Learn about vectors, matrices, and linear transformations—the fundamental building blocks of the subject. Matrix Operations: Dive into matrix operations. Explore techniques for matrix addition, multiplication, inversion, and determinant computation. Vector Spaces: Grasp the art of vector spaces and subspaces. Understand how to define, visualize, and analyze vector spaces for various applications. Eigenvalues and Eigenvectors: Explore the significance of eigenvalues and eigenvectors. Learn how they enable the analysis of dynamic systems and transformations. Linear Systems: Understand how linear algebra solves systems of linear equations. Explore techniques for Gaussian elimination, LU decomposition, and matrix factorization. Applications in Science and Engineering: Delve into real-world applications of linear algebra. Discover how it's applied in physics, computer graphics, data analysis, and more. Inner Product Spaces: Grasp the concepts of inner product spaces and orthogonality. Explore applications in geometric interpretations and least-squares solutions. Singular Value Decomposition: Explore the power of singular value decomposition. Understand how it enables data compression, noise reduction, and dimensionality reduction. Why This Book Matters: In a world driven by data and technological advancement, mastering linear algebra offers a competitive edge. "Mastering Linear Algebra" empowers students, researchers, scientists, and technology enthusiasts to leverage this fundamental mathematical language, enabling them to analyze and solve problems across diverse fields. Unlock the Power of Mathematical Insight: In the landscape of mathematics and science, linear algebra is the key to understanding complex relationships and transformations. "Mastering Linear Algebra" equips you with the knowledge needed to leverage linear algebra concepts, enabling you to solve intricate problems with clarity and precision. Whether you're a seasoned learner or new to the world of linear algebra, this book will guide you in building a solid foundation for effective mathematical analysis and application. Your journey to mastering linear algebra starts here. © 2023 Cybellium Ltd. All rights reserved. www.cybellium.com