http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Accuracy and stability of numerical algorithms
xxviii, 688 pages : illustrations ; 24 cm
Principles of Finite Precision Computation -- Relative Error and Significant Digits -- Sources of Errors -- Precision Versus Accuracy -- Backward and Forward Errors -- Conditioning -- Cancellation -- Solving a Quadratic Equation -- Computing the Sample Variance -- Solving Linear Equations -- Accumulation of Rounding Errors -- Instability Without Cancellation -- Increasing the Precision -- Cancellation of Rounding Errors -- Rounding Errors Can Be Beneficial -- Stability of an Algorithm Depends on the Problem -- Rounding Errors Are Not Random -- Designing Stable Algorithms -- Misconceptions -- Rounding Errors in Numerical Analysis -- Floating Point Arithmetic -- Floating Point Number System -- Model of Arithmetic -- IEEE Arithmetic -- Aberrant Arithmetics -- Exact Subtraction -- Fused Multiply-Add Operation -- Choice of Base and Distribution of Numbers -- Statistical Distribution of Rounding Errors -- Alternative Number Systems -- Elementary Functions -- Accuracy Tests -- Inner and Outer Products -- The Purpose of Rounding Error Analysis -- Running Error Analysis -- Notation for Error Analysis -- Matrix Multiplication -- Complex Arithmetic -- Miscellany -- Error Analysis Demystified -- Other Approaches -- Summation -- Summation Methods -- Error Analysis -- Compensated Summation -- Other Summation Methods -- Statistical Estimates of Accuracy -- Choice of Method -- Polynomials -- Horner's Method -- Evaluating Derivatives -- The Newton Form and Polynomial Interpolation -- Matrix Polynomials -- Norms -- Vector Norms.
Includes bibliographical references (pages 595-663) and indexes.