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Majosta Numerical Linear Algebra: Theorems, Proofs, and Python Implementations (Computational Mathematics Library)

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Description

A graduate-level reference that unites rigorous mathematics with hands-on computation. Twenty-four tightly written chapters carry the reader from floating-point arithmetic to large-scale parallel solvers, always pairing theorems and proofs with annotated Python code. Why this book? • Comprehensive coverage of LU and Cholesky factorization, QR decomposition, and Singular Value Decomposition (SVD) – the staples of every scientific computing and machine learning stack. • Complete treatments of iterative methods such as Conjugate Gradient, GMRES, and Lanczos-based eigenvalue algorithms, including advanced preconditioning strategies. • Up-to-date material on randomized linear algebra, low-rank approximation, and sketching – indispensable for modern data science pipelines. • Detailed chapters on GPU acceleration, communication-avoiding algorithms, and distributed memory implementations, giving readers a clear path from theory to high-performance code. • In-depth discussion of condition numbers, backward error analysis, and stability, providing the mathematical guarantees demanded in engineering and quantitative finance. • Every chapter closes with ready-to-run Python notebooks that reproduce all numerical examples and visualizations. Key contents Vector norms, spectral radius, and condition numbers IEEE floating-point and roundoff analysis Backward stability of Gaussian elimination Blocked and communication-optimal LU, QR, and Cholesky Least-squares, Tikhonov regularization, and linear regression Power, inverse, and Rayleigh quotient iterations for eigenvalues Bidiagonal SVD algorithms and sensitivity results Krylov subspace methods – CG, MINRES, GMRES, BiCGStab Preconditioning, algebraic multigrid, and spectral transformations Matrix functions – exponential, logarithm, and fractional powers Low-rank approximation for data compression and machine learning Randomized matrix multiplication, CUR, and RSVD

Product Specifications

Brand
Majosta
Format
hardcover
Domain
Amazon UK
Release Date
05 August 2025
Listed Since
06 August 2025

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