Computer solution of linear algebraic systems

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• graycat · Jul 8, 2018 · Recommends

  …eigenvectors, Hermitian, unitary, and the spectral decomposition! Right, the Halmos book is baby Hilbert space. Then look at some applied connections, e.g., George E.\ Forsythe and Cleve B.\ Moler, {\it Computer Solution of Linear Algebraic Systems,\/} Maybe spend an evening on the documentation of LINPACK. Some weekend of great fun, take a fast pass through the Gauss, ..., Stokes theorem parts of Tom M.\ Apostol, {\it Mathematical Analysis: A…

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• HilbertSpace · Dec 24, 2010 · Recommends

  …y^1) = b^1 + c^1 = b^1 + b - b^1 = b Of course, could do several steps of iteration here. This process is called 'iterative improvement'. This and more are in George E. Forsythe and Cleve B. Moler, 'Computer Solution of Linear Algebraic Systems', Prentice-Hall, Englewood Cliffs, 1967. E.g., pay close attention to 'partial pivoting'. Beware of the fact that Ax = b may have a solution but not a unique solution. If this is the case in your problem,…

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• graycat · Dec 12, 2013 · Recommends

  …---------------------------------------- If want to take numerical computations in linear algebra seriously, then consider the next book or something better if can find it George E. Forsythe and Cleve B. Moler, 'Computer Solution of Linear Algebraic Systems', Prentice-Hall, Englewood Cliffs, 1967. ======================================== Multivariate Statistics My main start with multivariate statistics was N. R. Draper and H. Smith, 'Applied Regression…

  on “Linear algebra tutorial in four pages” ↗
• graycat · Jul 3, 2020 · Recommends

  …of Richard Bellman, Introduction to Matrix Analysis: Second Edition. Bellman was famous for dynamic programming. For computations in linear algebra, consider George E. Forsythe and Cleve B. Moler, Computer Solution of Linear Algebraic Systems although now the Linpack materials might be a better starting point for numerical linear algebra. Numerical linear algebra is now a well developed specialized field, and the Linpack materials might…

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• NY_Entrepreneur · Aug 12, 2011 · Mentions

  …the connection with Gauss elimination! Why? Gauss elimination, for numerical stability, should emphasize careful selection of the 'pivot' elements, e.g., as in George E. Forsythe and Cleve B. Moler, 'Computer Solution of Linear Algebraic Systems', Prentice-Hall, Englewood Cliffs. and the simplex algorithm of linear programming does not have that freedom or luxury. So, each 'iteration' in the simplex algorithm is just an application of elementary…

  on “Milestone for MIT Press’s bestseller, "Introduction to Algorithms"” ↗
• graycat · Nov 17, 2018 · Mentions

  …Edition, Prentice-Hall, Englewood Cliffs, New Jersey, 1971. https://www.zuj.edu.jo/download/linear-algebra-2nd-edition-k... Halmos, Finite Dimensional Vector Spaces George E. Forsythe and Cleve B. Moler, Computer Solution of Linear Algebraic Systems Paul R. Halmos, Naive Set Theory, Van Nostrand, Princeton, NJ, 1960. More has been done since this book, but this book is a gorgeous introduction to axiomatic set theory. So, even people who want to…

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• graycat · Dec 23, 2017 · Mentions

  …specifically restricted my remarks to numerical linear algebra. Double precision inner product accumulation is a standard idea in numerical linear algebra, e.g., as in George E. Forsythe and Cleve B. Moler, Computer Solution of Linear Algebraic Systems. People have long struggled with accuracy in numerical linear algebra. At one time at the US National Bureau of Standards, the struggles were so severe that M. Newman wrote software for numerically…

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• graycat · Mar 12, 2015 · Mentions

  …cover to cover, including the parts on exterior algebra. Then I did that again from Spivak's Calculus on Manifolds -- right, a lot of both calculus and linear algebra. Then I got Forsythe and Moler, Computer Solution of Linear Algebraic Systems, read it cover to cover, directed a project in interval arithmetic for linear algebra, took a course in numerical analysis with a lot of linear algebra for solution of partial differential equations,…

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