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1: 3.2 Linear Algebra
§3.2 Linear Algebra
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§3.2(iii) Condition of Linear Systems
ā–ŗ ā–ŗThe p -norm of a matrix š€ = [ a j ā¢ k ] is … ā–ŗThen we have the a posteriori error bound …
2: 28.34 Methods of Computation
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  • (d)

    Solution of the matrix eigenvalue problem for each of the five infinite matrices that correspond to the linear algebraic equations (28.4.5)–(28.4.8) and (28.14.4). See Zhang and Jin (1996, pp. 479–482) and §3.2(iv).

  • ā–ŗ
  • (d)

    Solution of the systems of linear algebraic equations (28.4.5)–(28.4.8) and (28.14.4), with the conditions (28.4.9)–(28.4.12) and (28.14.5), by boundary-value methods (§3.6) to determine the Fourier coefficients. Subsequently, the Fourier series can be summed with the aid of Clenshaw’s algorithm (§3.11(ii)). See Meixner and Schäfke (1954, §2.87). This procedure can be combined with §28.34(ii)(d).

  • 3: Philip J. Davis
    ā–ŗThis immediately led to discussions among some of the project members about what might be possible, and the discovery that some interactive graphics work had already been done for the NIST Matrix Market, a publicly available repository of test matrices for comparing the effectiveness of numerical linear algebra algorithms. …
    4: Bibliography I
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  • Y. Ikebe, Y. Kikuchi, I. Fujishiro, N. Asai, K. Takanashi, and M. Harada (1993) The eigenvalue problem for infinite compact complex symmetric matrices with application to the numerical computation of complex zeros of J 0 ā¢ ( z ) i ā¢ J 1 ā¢ ( z ) and of Bessel functions J m ā¢ ( z ) of any real order m . Linear Algebra Appl. 194, pp. 35–70.
  • 5: Bibliography T
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  • L. N. Trefethen and D. Bau (1997) Numerical Linear Algebra. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
  • 6: Bibliography H
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  • J. H. Hubbard and B. B. Hubbard (2002) Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach. 2nd edition, Prentice Hall Inc., Upper Saddle River, NJ.
  • 7: Bibliography
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  • S. Axler (2015) Linear algebra done right. Third edition, Undergraduate Texts in Mathematics, Springer, Cham.
  • 8: Bibliography M
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  • Meta.Numerics (website) David Wright’s software package for .NET programming language
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  • mpmath (free python library)
  • 9: 2.6 Distributional Methods
    ā–ŗIt is easily seen that K + forms a commutative, associative linear algebra. …
    10: Bruce R. Miller
    ā–ŗThere, he carried out research in non-linear dynamics and celestial mechanics, developing a specialized computer algebra system for high-order Lie transformations. …