Titlebook: Complexity and Real Computation; Lenore Blum,Felipe Cucker,Steve Smale Textbook 1998 Springer Science+Business Media New York 1998 algorit

使害怕

Chain Statistics of Amorphous PolymersClassical complexity theory deals primarily with combinatorial (discrete, integer) problems. We extend the theory here to consider a wider class of problems.

oracle

Patrice E. A. Turchi,Antonios GonisThe condition number of an invertible real or complex . x . matrix A is defined as.where ‖A‖ is the operator norm.and ℝ. or ℂ. is given the usual inner product. The condition number measures the relative error in the solution of the system of linear equations

obligation

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https://doi.org/10.1007/978-3-642-82135-6The focus of this chapter is on the result that the complexity of a continuation algorithm can be bounded essentially by the square of the condition number of the homotopy.

EPT

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Definitions and First Properties of ComputationWe begin the development of our theory of computation with the definition of a . over a ring. Although it is necessary to define a . to be a more general object in order to fully develop a uniform theory —in particular with regard to complexity issues— a great deal can already be gleaned from the finite-dimensional case.

admission

Decision Problems and Complexity over a RingClassical complexity theory deals primarily with combinatorial (discrete, integer) problems. We extend the theory here to consider a wider class of problems.

ARBOR

Condition Numbers and the Loss of Precision of Linear EquationsThe condition number of an invertible real or complex . x . matrix A is defined as.where ‖A‖ is the operator norm.and ℝ. or ℂ. is given the usual inner product. The condition number measures the relative error in the solution of the system of linear equations

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The Condition Number in ℙ(,,)In this chapter we study the condition numbers μ(.) and μ.(.) as functions on ℙ(..) in greater depth. Our main theorem is proven in Section 13.6.

Cougar

Complexity and the Condition NumberThe focus of this chapter is on the result that the complexity of a continuation algorithm can be bounded essentially by the square of the condition number of the homotopy.