An algorithm for the best approximation by elements of a polyhedral set in banach spaces

1983 ◽  
Vol 6 (3) ◽  
pp. 273-285 ◽  
Author(s):  
Constantin Zǎlinescu
Keyword(s):  
Banach Spaces ◽  
Best Approximation ◽  
The Best Approximation ◽  
Polyhedral Set

Intracranial volume-pressure relationship in man

1982 ◽  
Vol 56 (4) ◽  
pp. 524-528 ◽  
Author(s):  
Joseph Th. J. Tans ◽  
Dick C. J. Poortvliet
Keyword(s):  
Best Approximation ◽  
Continuous Monitoring ◽  
Fluid Pressure ◽  
Constant Term ◽  
Volume Index ◽  
Intracranial Volume ◽  
Content Type ◽  
The Best Approximation ◽  
Ventricular Fluid Pressure ◽  
Fine Print

✓ The pressure-volume index (PVI) was determined in 40 patients who underwent continuous monitoring of ventricular fluid pressure. The PVI value was calculated using different mathematical models. From the differences between these values, it is concluded that a monoexponential relationship with a constant term provides the best approximation of the PVI.

scholarly journals A note on best approximation and invertibility of operators on uniformly convex Banach spaces

1991 ◽  
Vol 14 (3) ◽  
pp. 611-614 ◽  
Author(s):  
James R. Holub
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Banach Spaces ◽  
Best Approximation ◽  
Bounded Linear Operator ◽  
Convex Banach Space ◽  
Sufficient Condition ◽  
Uniformly Convex ◽  
Bounded Linear ◽  
Uniformly Convex Banach Spaces

It is shown that ifXis a uniformly convex Banach space andSa bounded linear operator onXfor which‖I−S‖=1, thenSis invertible if and only if‖I−12S‖<1. From this it follows that ifSis invertible onXthen either (i)dist(I,[S])<1, or (ii)0is the unique best approximation toIfrom[S], a natural (partial) converse to the well-known sufficient condition for invertibility thatdist(I,[S])<1.

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