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André-Louis Cholesky

Author : Claude Brezinski

Publisher : Springer

Page : 340 pages

File Size : 10,23 MB

Release : 2014-08-06

Category : Mathematics

ISBN : 3319081357

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Book Description

This book traces the life of Cholesky (1875-1918), and gives his family history. After an introduction to topography, an English translation of an unpublished paper by him where he explained his method for linear systems is given, studied and replaced in its historical context. His other works, including two books, are also described as well as his involvement in teaching at a superior school by correspondence. The story of this school and its founder, Léon Eyrolles, are addressed. Then, an important unpublished book of Cholesky on graphical calculation is analyzed in detail and compared to similar contemporary publications. The biography of Ernest Benoit, who wrote the first paper where Cholesky ́s method is explained, is provided. Various documents, highlighting the life and the personality of Cholesky, end the book.



Numerical Linear Algebra and Applications

Author : Biswa Nath Datta

Publisher : SIAM

Page : 545 pages

File Size : 42,42 MB

Release : 2010-02-04

Category : Mathematics

ISBN : 0898716853

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Book Description

An undergraduate textbook that highlights motivating applications and contains summary sections, examples, exercises, online MATLAB codes and a MATLAB toolkit. All the major topics of computational linear algebra are covered, from basic concepts to advanced topics such as the quadratic eigenvalue problem in later chapters.



Matrix Analysis and Applied Linear Algebra

Author : Carl D. Meyer

Publisher : SIAM

Page : 1006 pages

File Size : 21,59 MB

Release : 2023-05-18

Category : Mathematics

ISBN : 1611977444

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Book Description

This second edition has been almost completely rewritten to create a textbook designed so instructors can determine the degree of rigor and flexible enough for a one- or two-semester course. The author achieves this by increasing the level of sophistication as the text proceeds from traditional first principles in the early chapters to theory and applications in the later ones, and by ensuring that material at any point is not dependent on subsequent developments. While theorems and proofs are highlighted, the emphasis is on applications. The author provides carefully constructed exercises ranging from easy to moderately challenging to difficult, many of which condition students for topics that follow. An accompanying book, Matrix Analysis and Applied Linear Algebra, Second Edition, Study and Solutions Guide, contains complete solutions and discussions of each exercise; and historical remarks that focus on the personalities of the individuals who created and contributed to the subject's development. This book is designed for use in either a one- or two-term linear algebra course. It can also serve as a reference to anyone who needs to use or apply linear algebra.



An Introduction to Numerical Methods and Analysis

Author : James F. Epperson

Publisher : John Wiley & Sons

Page : 579 pages

File Size : 45,73 MB

Release : 2013-06-06

Category : Mathematics

ISBN : 1118626230

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Book Description

Praise for the First Edition ". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises." —Zentrablatt Math ". . . carefully structured with many detailed worked examples . . ." —The Mathematical Gazette ". . . an up-to-date and user-friendly account . . ." —Mathematika An Introduction to Numerical Methods and Analysis addresses the mathematics underlying approximation and scientific computing and successfully explains where approximation methods come from, why they sometimes work (or don't work), and when to use one of the many techniques that are available. Written in a style that emphasizes readability and usefulness for the numerical methods novice, the book begins with basic, elementary material and gradually builds up to more advanced topics. A selection of concepts required for the study of computational mathematics is introduced, and simple approximations using Taylor's Theorem are also treated in some depth. The text includes exercises that run the gamut from simple hand computations, to challenging derivations and minor proofs, to programming exercises. A greater emphasis on applied exercises as well as the cause and effect associated with numerical mathematics is featured throughout the book. An Introduction to Numerical Methods and Analysis is the ideal text for students in advanced undergraduate mathematics and engineering courses who are interested in gaining an understanding of numerical methods and numerical analysis.



Accuracy and Stability of Numerical Algorithms

Author : Nicholas J. Higham

Publisher : SIAM

Page : 710 pages

File Size : 25,9 MB

Release : 2002-01-01

Category : Mathematics

ISBN : 9780898718027

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Book Description

Accuracy and Stability of Numerical Algorithms gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory, and rounding error analysis, all enlivened by historical perspective and informative quotations. This second edition expands and updates the coverage of the first edition (1996) and includes numerous improvements to the original material. Two new chapters treat symmetric indefinite systems and skew-symmetric systems, and nonlinear systems and Newton's method. Twelve new sections include coverage of additional error bounds for Gaussian elimination, rank revealing LU factorizations, weighted and constrained least squares problems, and the fused multiply-add operation found on some modern computer architectures.



Numerical Methods in Engineering

Author : Amiya K. Jana

Publisher : Cambridge University Press

Page : 685 pages

File Size : 34,33 MB

Release : 2024-07-31

Category : Mathematics

ISBN : 1009211803

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Book Description

This textbook strikes a balance between theory and practice to introduce engineering students to numerical methods and their process applications.



Numerical Linear Algebra with Applications

Author : William Ford

Publisher : Academic Press

Page : 629 pages

File Size : 25,21 MB

Release : 2014-09-14

Category : Mathematics

ISBN : 0123947847

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Book Description

Numerical Linear Algebra with Applications is designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, using MATLAB as the vehicle for computation. The book contains all the material necessary for a first year graduate or advanced undergraduate course on numerical linear algebra with numerous applications to engineering and science. With a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions, this book is ideal for solving real-world problems. The text consists of six introductory chapters that thoroughly provide the required background for those who have not taken a course in applied or theoretical linear algebra. It explains in great detail the algorithms necessary for the accurate computation of the solution to the most frequently occurring problems in numerical linear algebra. In addition to examples from engineering and science applications, proofs of required results are provided without leaving out critical details. The Preface suggests ways in which the book can be used with or without an intensive study of proofs. This book will be a useful reference for graduate or advanced undergraduate students in engineering, science, and mathematics. It will also appeal to professionals in engineering and science, such as practicing engineers who want to see how numerical linear algebra problems can be solved using a programming language such as MATLAB, MAPLE, or Mathematica. Six introductory chapters that thoroughly provide the required background for those who have not taken a course in applied or theoretical linear algebra Detailed explanations and examples A through discussion of the algorithms necessary for the accurate computation of the solution to the most frequently occurring problems in numerical linear algebra Examples from engineering and science applications



Advanced Engineering Mathematics

Author : Dennis G. Zill

Publisher : Jones & Bartlett Publishers

Page : 1047 pages

File Size : 37,96 MB

Release : 2018

Category : Mathematics

ISBN : 1284105903

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Book Description

Modern and comprehensive, the new sixth edition of Zill’s Advanced Engineering Mathematics is a full compendium of topics that are most often covered in engineering mathematics courses, and is extremely flexible to meet the unique needs of courses ranging from ordinary differential equations to vector calculus. A key strength of this best-selling text is Zill’s emphasis on differential equation as mathematical models, discussing the constructs and pitfalls of each.



Probability and Random Processes

Author : Geoffrey Grimmett

Publisher : Oxford University Press, USA

Page : 682 pages

File Size : 34,17 MB

Release : 2020-07-16

Category :

ISBN : 0198847602

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Book Description

The fourth edition of this successful text provides an introduction to probability and random processes, with many practical applications. It is aimed at mathematics undergraduates and postgraduates, and has four main aims. US � To provide a thorough but straightforward account of basic probability theory, giving the reader a natural feel for the subject unburdened by oppressive technicalities.BE � To discuss important random processes in depth with many examples.BE � To cover a range of topics that are significant and interesting but less routine.BE � To impart to the beginner some flavour of advanced work.BE UE OP The book begins with the basic ideas common to most undergraduate courses in mathematics, statistics, and science. It ends with material usually found at graduate level, for example, Markov processes, (including Markov chain Monte Carlo), martingales, queues, diffusions, (including stochastic calculus with It�'s formula), renewals, stationary processes (including the ergodic theorem), and option pricing in mathematical finance using the Black-Scholes formula. Further, in this new revised fourth edition, there are sections on coupling from the past, L�vy processes, self-similarity and stability, time changes, and the holding-time/jump-chain construction of continuous-time Markov chains. Finally, the number of exercises and problems has been increased by around 300 to a total of about 1300, and many of the existing exercises have been refreshed by additional parts. The solutions to these exercises and problems can be found in the companion volume, One Thousand Exercises in Probability, third edition, (OUP 2020).CP



LINPACK Users' Guide

Author : J. J. Dongarra

Publisher : SIAM

Page : 375 pages

File Size : 50,93 MB

Release : 1979-01-01

Category : Computers

ISBN : 9781611971811

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Book Description

The authors of this carefully structured guide are the principal developers of LINPACK, a unique package of Fortran subroutines for analyzing and solving various systems of simultaneous linear algebraic equations and linear least squares problems. This guide supports both the casual user of LINPACK who simply requires a library subroutine, and the specialist who wishes to modify or extend the code to handle special problems. It is also recommended for classroom work.