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001451562 001__ 1451562
001451562 003__ OCoLC
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001451562 019__ $$a1352967882
001451562 020__ $$a9783031081217$$q(electronic bk.)
001451562 020__ $$a3031081218$$q(electronic bk.)
001451562 020__ $$z303108120X
001451562 020__ $$z9783031081200
001451562 0247_ $$a10.1007/978-3-031-08121-7$$2doi
001451562 035__ $$aSP(OCoLC)1352790146
001451562 040__ $$aYDX$$beng$$cYDX$$dGW5XE$$dEBLCP$$dOCLCF$$dUKAHL$$dOCLCQ
001451562 049__ $$aISEA
001451562 050_4 $$aQA297
001451562 08204 $$a518$$223/eng/20221215
001451562 1001_ $$aStewart, David,$$d1961-
001451562 24510 $$aNumerical analysis :$$ba graduate course /$$cDavid E. Stewart.
001451562 260__ $$aCham, Switzerland :$$bSpringer,$$c2022.
001451562 300__ $$a1 online resource
001451562 4901_ $$aCMS/CAIMS Books in Mathematics ;$$vv.4
001451562 504__ $$aIncludes bibliographical references and index.
001451562 5050_ $$aIntro -- Preface -- Contents -- 1 Basics of Numerical Computation -- 1.1 How Computers Work -- 1.1.1 The Central Processing Unit -- 1.1.2 Code and Data -- 1.1.3 On Being Correct -- 1.1.4 On Being Efficient -- 1.1.5 Recursive Algorithms and Induction -- 1.1.6 Working in Groups: Parallel Computing -- 1.1.7 BLAS and LAPACK -- Exercises -- 1.2 Programming Languages -- 1.2.1 MATLABTM -- 1.2.2 Julia -- 1.2.3 Python -- 1.2.4 C/C++ and Java -- 1.2.5 Fortran -- Exercises -- 1.3 Floating Point Arithmetic -- 1.3.1 The IEEE Standards -- 1.3.2 Correctly Rounded Arithmetic
001451562 5058_ $$a1.3.3 Future of Floating Point Arithmetic -- Exercises -- 1.4 When Things Go Wrong -- 1.4.1 Underflow and Overflow -- 1.4.2 Subtracting Nearly Equal Quantities -- 1.4.3 Numerical Instability -- 1.4.4 Adding Many Numbers -- Exercises -- 1.5 Measuring: Norms -- 1.5.1 What Is a Norm? -- 1.5.2 Norms of Functions -- Exercises -- 1.6 Taylor Series and Taylor Polynomials -- 1.6.1 Taylor Series in One Variable -- 1.6.2 Taylor Series and Polynomials in More than One Variable -- 1.6.3 Vector-Valued Functions -- Exercises -- Project -- 2 Computing with Matrices and Vectors -- 2.1 Solving Linear Systems
001451562 5058_ $$a2.1.1 Gaussian Elimination -- 2.1.2 LU Factorization -- 2.1.3 Errors in Solving Linear Systems -- 2.1.4 Pivoting and PA=LU -- 2.1.5 Variants of LU Factorization -- Exercises -- 2.2 Least Squares Problems -- 2.2.1 The Normal Equations -- 2.2.2 QR Factorization -- Exercises -- 2.3 Sparse Matrices -- 2.3.1 Tridiagonal Matrices -- 2.3.2 Data Structures for Sparse Matrices -- 2.3.3 Graph Models of Sparse Factorization -- 2.3.4 Unsymmetric Factorizations -- Exercises -- 2.4 Iterations -- 2.4.1 Classical Iterations -- 2.4.2 Conjugate Gradients and Krylov Subspaces
001451562 5058_ $$a2.4.3 Non-symmetric Krylov Subspace Methods -- Exercises -- 2.5 Eigenvalues and Eigenvectors -- 2.5.1 The Power Method & Google -- 2.5.2 Schur Decomposition -- 2.5.3 The QR Algorithm -- 2.5.4 Singular Value Decomposition -- 2.5.5 The Lanczos and Arnoldi Methods -- Exercises -- 3 Solving nonlinear equations -- 3.1 Bisection method -- 3.1.1 Convergence -- 3.1.2 Robustness and reliability -- Exercises -- 3.2 Fixed-point iteration -- 3.2.1 Convergence -- 3.2.2 Robustness and reliability -- 3.2.3 Multivariate fixed-point iterations -- Exercises -- 3.3 Newton's method
001451562 5058_ $$a3.3.1 Convergence of Newton's method -- 3.3.2 Reliability of Newton's method -- 3.3.3 Variant: Guarded Newton method -- 3.3.4 Variant: Multivariate Newton method -- Exercises -- 3.4 Secant and hybrid methods -- 3.4.1 Convenience: Secant method -- 3.4.2 Regula Falsi -- 3.4.3 Hybrid methods: Dekker's and Brent's methods -- Exercises -- 3.5 Continuation methods -- 3.5.1 Following paths -- 3.5.2 Numerical methods to follow paths -- Exercises -- Project -- 4 Approximations and Interpolation -- 4.1 Interpolation-Polynomials -- 4.1.1 Polynomial Interpolation in One Variable
001451562 506__ $$aAccess limited to authorized users.
001451562 520__ $$aThis book aims to introduce graduate students to the many applications of numerical computation, explaining in detail both how and why the included methods work in practice. The text addresses numerical analysis as a middle ground between practice and theory, addressing both the abstract mathematical analysis and applied computation and programming models instrumental to the field. While the text uses pseudocode, Matlab and Julia codes are available online for students to use, and to demonstrate implementation techniques. The textbook also emphasizes multivariate problems alongside single-variable problems and deals with topics in randomness, including stochastic differential equations and randomized algorithms, and topics in optimization and approximation relevant to machine learning. Ultimately, it seeks to clarify issues in numerical analysis in the context of applications, and presenting accessible methods to students in mathematics and data science. .
001451562 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed December 15, 2022).
001451562 650_0 $$aNumerical analysis.
001451562 650_0 $$aDifferential equations.
001451562 655_0 $$aElectronic books.
001451562 77608 $$iPrint version: $$z303108120X$$z9783031081200$$w(OCoLC)1317832646
001451562 830_0 $$aCMS/CAIMS books in mathematics ;$$vv. 4.
001451562 852__ $$bebk
001451562 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-08121-7$$zOnline Access$$91397441.1
001451562 909CO $$ooai:library.usi.edu:1451562$$pGLOBAL_SET
001451562 980__ $$aBIB
001451562 980__ $$aEBOOK
001451562 982__ $$aEbook
001451562 983__ $$aOnline
001451562 994__ $$a92$$bISE