Abstract
Some relevant mathematical results are collected in this chapter. These results find a wide application within the realm of analysis, synthesis and optimization of mechanisms. Often, rigorous proofs are not provided; however a reference list is given at the end of the chapter, where the interested reader can find the required details.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Lang S., Linear Algebra, Addison-Wesley Publishing Co., Menlo Park, 1970, pp. 39 and 40.
Lang S., op. cit., pp. 99 and 100
Finkbeiner, D.F., Matrices and Linear Transformations, W.H. Freeman and Company, San Francisco, 1960, pp. 139–142
Halmos, P.R., Finite-Dimensional Vector Spaces, Springer-Verlag, N. York, 1974.
Businger P. and G.H. Golub, “Linear Least Squares Solutions by Householder Transformations”, in Wilkinson J.H. and C. Reinsch, eds., Handbook for Automatic Computation, Vol. II, Springer-Verlag, N. York, 1971, pp. 111–118
Stewart, G.W., Introduction to Matrix Computations, Academic Press, N.York, 1973, pp. 208–249.
Soderstrom T. and G.W. Stewart, “On the numerical properties of an iterative method for computing the Moore-Penrose generalized inverse”, SIAM J. on Numerical Analysis, Vol. II, No. 1, March 1974.
Brand L., Advanced Calculus, John Wiley and Sons, Inc., N. York, 1955, pp. 147–197.
Luenberger, D.G., Optimization by Vector Space Methods, John Wiley and Sons, Inc., N. York, 1969, pp. 8, 49–52
Varga, R.S., Matrix Iterative Analysis, Prentice Hall, Inc., Englewood Cliffs, 1962, pp. 56–160
Forsythe, G.E. and C.B. Moler, Computer Solution of Linear Algebraic Systems, Prentice Hall, Inc., Englewood Cliffs, 1967, pp. 27–33
Moler C.B., “Algorithm Linear Equation Solver OF 4)” Communications of the ACM, Vol. 15, Number 4, April 1973, p. 274.
Björck A. and G. Dahlquist, Numerical Methods, Prentice-Hall, Inc., Englewood Cliffs, 1974, pp. 201–206.
Moler C.B., Matrix Eigenvalue and Least Square Computations,Computer Science Departament, Stanford University, Stanford, California, 1973 pp. 4. 1–4. 15
Isaacson, E. and H. B. Keller, Analysis of Numerical Methods, John Wiley and Sons, Inc., N. York, 1966, pp. 85–123
Angeles, J., “Optimal synthesis of linkages using Householder reflections”, Proceedings of the Fifth World Congress on the Theory of Machines and Mechanisms, vol. I, Montreal, Canada, July 8–13, 1979, pp. 111’-114.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1982 Springer-Verlag Berlin, Heidelberg
About this chapter
Cite this chapter
Angeles, J. (1982). Mathematical Preliminaries. In: Spatial Kinematic Chains. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-48819-1_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-48819-1_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-48821-4
Online ISBN: 978-3-642-48819-1
eBook Packages: Springer Book Archive