Pdf J.h.wilkinson C.reinsch Handbook For Automatic Computation Pdf

 



  • Handbook for Automatic Computation Volume II: Linear Algebra. Authors: Wilkinson, John H., Reinsch, C. Editors: Editor-in-chief: Bauer, Friedrich L.
  • Pdf J.h.wilkinson C.reinsch Handbook For Automatic Computation Pdf Template. Jul 18, 2006 Plasmon Resonance with Finite Frequencies: a Validation of the Quasi-static Approximation for Diametrically Small Inclusions Crank-Nicolson Alternative Direction Implicit Method for Space-Fractional Diffusion Equations with Nonseparable Coefficients.
Pdf J.h.wilkinson C.reinsch Handbook For Automatic Computation Pdf

Constant-Round Interactive Proofs for Delegating Computation Convergence of Vortex Methods for Euler’s Equations. II Perturbations of Time Shifts in Signal Apparition An Adaptive Time-Stepping Strategy for the Molecular Beam Epitaxy Models.

Algorithms for triangular decomposition of block Hankel and Toeplitz matrices with application to factoring positive matrix polynomials


Author:J. Rissanen
Journal:Math. Comp. 27 (1973), 147-154
MSC:Primary 65F30
DOI:https://doi.org/10.1090/S0025-5718-1973-0329235-5
MathSciNet review:0329235
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Abstract: Algorithms are given for calculating the block triangular factors and and the block diagonal factor D in the factorizations and of block Hankel and Toeplitz matrices R. The algorithms require operations when R is an -matrix of -blocks.

As an application, an iterative method is described for factoring -matrix valued positive polynomials , as , where is outer.

Pdf J.h.wilkinson C.reinsch Handbook For Automatic Computation Pdf File

  • [1]N. Levinson, 'The Wiener RMS error criterion in filter design and prediction,' Appendix B of N. Wiener's book Extrapolation, Interpolation, and Smoothing Stationary Time Series with Engineering Applications, Wiley, New York, 1949, pp. 129-148.
  • [2]RalphA. Wiggins and EndersA. Robinson, Recursive solution to the multichannel filteringproblem, J. Geophys. Res. 70 (1965), 1885–1891.MR183107
  • [3]JamesL. Phillips, The triangular decomposition of Hankelmatrices, Math. Comp.25 (1971), 559–602. MR295553, https://doi.org/10.1090/S0025-5718-1971-0295553-0
  • [4]AllenDevinatz, The factorization of operator valued functions, Ann.of Math. (2) 73 (1961), 458–495. MR126702, https://doi.org/10.2307/1970313
  • [5]FriedrichL. Bauer, Ein direktes Iterationsverfahren zur Hurwitz-Zerlegungeines Polynoms, Arch. Elek. Übertr. 9 (1955),285–290 (German). MR0076447
  • [6]Handbook for automatic computation. Vol. II, Springer-Verlag, NewYork-Heidelberg, 1971. Linear algebra; Compiled by J. H. Wilkinson and C.Reinsch; Die Grundlehren der Mathematischen Wissenschaften, Band 186. MR0461856
  • [7]J.Rissanen and L.Barbosa, Properties of infinite covariance matrices and stabilityof optimum predictors, Information Sci. 1(1968/1969), 221–236. MR0243711, https://doi.org/10.1016/s0020-0255(69)80009-5

Pdf J.h.wilkinson C.reinsch Handbook For Automatic Computation Pdf Free

Extrapolation, Interpolation, and Smoothing Stationary Time Series with Engineering Applications, Wiley, New York, 1949, pp. 129-148.
[2]
R. A. Wiggins & E. A. Robinson, 'Recursive solution to the multichannel filtering problem,' J. Geophys. Res., v. 70, 1965, pp. 1885-1891. MR 32 #589. MR 0183107 (32:589)
[3]
J. L. Phillips, 'The triangular decomposition of Hankel matrices,' Math Comp., v. 25, 1971, pp. 599-602. MR 0295553 (45:4619)
[4]
A. Devinatz, 'The factorization of operator valued functions,' Ann. of Math., (2), v. 73, 1961, pp. 458-495. MR 23 #A3997. MR 0126702 (23:A3997)
[5]
F. L. Bauer, 'Ein direktes Iterationsverfahren zur Hurwitz-Zerlegung eines Polynoms,' Arch. Elek. Übertr., v. 9, 1955, pp. 285-290. MR 17, 900. MR 0076447 (17:900e)
[6]
J. H. Wilkinson & C. Reinsch, Handbook for Automatic Computation. Vol. II. Linear Algebra, Springer-Verlag, New York, 1971. MR 0461856 (57:1840)
[7]
J. Rissanen & L. Barbosa, 'Properties of infinite covariance matrices and stability of optimum predictors,' Information Sci., v. 1, 1969, pp. 221-236. MR 39 #5032. MR 0243711 (39:5032)

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Additional Information
DOI:https://doi.org/10.1090/S0025-5718-1973-0329235-5
Keywords:Hankel and Toeplitz matrices,triangular decomposition of matrices
Article copyright:© Copyright 1973American Mathematical Society

Pdf J.h.wilkinson C.reinsch Handbook For Automatic Computation Pdf Template

Automatic computing has undergone drastic changes since the pioneering days of the early Fifties, one of the most obvious being that today the majority of computer programs are no longer written in machine code but in some programming language like FORTRAN or ALGOL. However, as desirable as the time-saving achieved in this way may be, still a high proportion of the preparatory work must be attributed to activities such as error estimates, stability investigations and the like, and for these no programming aid whatsoever can be of help. In this respect, ALGOL, as an internationally standardized notation which avoids computer-oriented concepts, provides another advantage, not often mentioned, but one which was already the guiding principle at the very beginning of the programming language venture: indeed, a correct ALGOL program is the abstractum of a computing process for which the necessary analyses have already been performed. It is the very purpose of this Handbook to establish such abstract formulations of certain computing processes. Therefore, numerical methods given in this Hand­ book in the form of ALGOL procedures may be put to immediate use wherever ALGOL is known and understood; in fact, application of such a method reduces to little more than calling the corresponding procedure.