Accuracy and Stability Book Page
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Companion page for Nicholas Higham's Accuracy and Stability of Numerical Algorithms (SIAM, 2nd ed.), with contents, errata, and supporting material for the standard reference on rounding error analysis, backward stability, and conditioning in floating-point computation.
More resources on Numerical Stability
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
Nick Higham's Numerical Analysis Blog
Blog by the late Nicholas Higham with concise expository posts on floating-point arithmetic, rounding error analysis, matrix functions, and numerical linear algebra, including his "What Is" series. Gives clear explanations of stability, conditioning, and backward error.
Accuracy and Stability of Numerical Algorithms, 2nd Edition
The terminal rung: once a learner can compute QR three ways, this is where the question of which one is actually trustworthy, and by how much, gets a proven answer. Rounding-error analysis reference whose QR chapter proves backward stability of Householder and Givens triangularization, quantifies loss of orthogonality in classical versus modified Gram-Schmidt, and treats column pivoting plus least-squares perturbation bounds.
Gaussian Elimination (MIMS EPrint 2011.16)
Ten-page survey explaining why Gaussian elimination computes an LU factorization and what that viewpoint buys, then covering pivoting strategies, growth factors, backward error bounds, matrix classes needing no pivoting, and blocked LAPACK-style implementations.
Nick Higham's "What Is" Series
Nicholas Higham's explainer series defines the working vocabulary of numerical computing: floating-point arithmetic, rounding error, condition numbers, backward error, numerical stability, matrix factorizations and matrix functions. Roughly a hundred short entries, each a few pages, also collected as PDFs.