Numerical Analysis Surveys

• Goldstine, H. H. (2012). A History of Numerical Analysis from the 16th through the 19th Century. Springer Science & Business Media.
• Brezinski, C., & Wuytack, L. (2012). Numerical analysis: Historical developments in the 20th century. Elsevier.
• Cipra, B. A. (2000). The best of the 20th century: Editors name top 10 algorithms. SIAM News, 33(4), 1-2.
• Dongarra, J., & Sullivan, F. (2000). Guest editors’ introduction: The top 10 algorithms. Computing in Science & Engineering, 2(1), 22.

Validated Numerics

• Alefeld, G., & Mayer, G. (2000). Interval analysis: theory and applications. Journal of computational and applied mathematics, 121(1-2), 421-464.
• Hargreaves, G. I. (2002). Interval analysis in MATLAB. Numerical Algorithms, (2009.1).
• Rump, S. M. (2010). Verification methods: Rigorous results using floating-point arithmetic. Acta Numerica, 19, 287-449.

Affine Arithmetic

• L. H. de Figueiredo and J. Stolfi (2004) "Affine arithmetic: concepts and applications." Numerical Algorithms 37 (1–4), 147–158.
• Nedialkov, N. S., Kreinovich, V., & Starks, S. A. (2004). Interval arithmetic, affine arithmetic, Taylor series methods: why, what next?. Numerical Algorithms, 37(1-4), 325-336.

和文

• 精度保証付き数値計算と kv ライブラリ
• 常微分方程式の精度保証付き数値解法
• 精度保証ノート
• 計算機援用証明と精度保証付き数値計算
• 高信頼・高精度・高可搬な数値計算法の研究
• 非線形方程式の解の精度保証付き数値計算に関する研究

Numerical Integration

• Gautschi, W. (1981). A survey of Gauss-Christoffel quadrature formulae. In EB Christoffel (pp. 72-147). Birkhäuser, Basel.
• Ioakimidis, N. I. (1987). Quadrature methods for the determination of zeros of transcendental functions-a review. In Numerical Integration (pp. 61-82). Springer, Dordrecht.
• Gander, W., & Gautschi, W. (2000). Adaptive quadrature—revisited. BIT Numerical Mathematics, 40(1), 84-101.
• Trefethen, L. N. (2008). Is Gauss quadrature better than Clenshaw–Curtis?. SIAM Review, 50(1), 67-87.
• Notaris, S. E. (2016). Gauss–Kronrod quadrature formulae–a survey of fifty years of research. Electron. Trans. Numer. Anal, 45, 371-404.

ODE

• Butcher, J. C. (2000). Numerical methods for ordinary differential equations in the 20th century. Journal of Computational and Applied Mathematics, 125(1-2), 1-29.
• Ahnert, K., & Mulansky, M. (2011, September). Odeint–solving ordinary differential equations in C++. In AIP Conference Proceedings (Vol. 1389, No. 1, pp. 1586-1589). AIP.

DAE

• Marz, R. (1992). Numerical methods for differential algebraic equations. Acta Numerica, 1, 141-198.

DDE

• Zennaro, M. (1995). Delay differential equations: theory and numerics. Theory and numerics of ordinary and partial differential equations, 291-333.

Numerical Linear Algebra

• Varga, R. S. (1976). M-matrix theory and recent results in numerical linear algebra. In Sparse Matrix Computations (pp. 375-387). Academic Press.
• A survey of condition number estimation for triangular matrices, NJ Higham - SIAM Review, 1987.
• Saad, Y., & Van Der Vorst, H. A. (2000). Iterative solution of linear systems in the 20th century. Journal of Computational and Applied Mathematics, 123(1-2), 1-33.

Matrix Exponential

• Moler, C., & Van Loan, C. (1978). Nineteen dubious ways to compute the exponential of a matrix. SIAM Review, 20(4), 801-836.
• Moler, C., & Van Loan, C. (2003). Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM Review, 45(1), 3-49.
• The scaling and squaring method for the matrix exponential revisited, NJ Higham - SIAM Journal on Matrix Analysis and Applications, 2005.

EVP

• Golub, G. H., & Van der Vorst, H. A. (2000). Eigenvalue computation in the 20th century. Journal of Computational and Applied Mathematics, 123(1-2), 35-65.
• NLEVP: A collection of nonlinear eigenvalue problems, T Betcke, NJ Higham, V Mehrmann, C Schröder et al. - ACM Transactions on Mathematical Software (TOMS), 2013.

Slides

• Bringing New Algorithms in Numerical Linear Algebra to Industry
• Numerical Linear Algebra in the UK: From Cayley to Exascale Computing
• Numerical Linear Algebra Routines for Emerging Computer Architectures
• Advances in high accuracy matrix computations

Function of Matrices

• Computation of matrix gamma function
• The Matrix Logarithm: from Theory to Computation
• Functions of a Matrix: Theory, Applications and Computation
• How and How Not to Compute the Exponential of a Matrix

和文

• 連立一次方程式の数値解に対する精度保証付き数値計算法
• 事前誤差評価を用いた線形計算の精度保証–誤差解析から大規模計算まで–
• 行列の固有値問題
• 連立1次方程式 II,—反復法—
• 連立1次方程式 III —自分が使うための線型代数—

Convergence Acceleration

• Acceleration Methods for Slowly Convergent Sequences and their Applications, January 1993
• Brezinski, C. (1996). Extrapolation algorithms and Padé approximations: a historical survey. Applied Numerical Mathematics, 20(3), 299-318.
• Brezinski, C. (2001). Convergence acceleration during the 20th century. Numerical Analysis: Historical Developments in the 20th Century, 113-133.
• Brezinski, C., & Redivo-Zaglia, M. (2019). The genesis and early developments of Aitken’s process, Shanks transformation, the \epsilon-algorithm, and related fixed point methods. Numerical Algorithms, 80(1), 11-133.