Learn More
Compared to standard numerical methods for initial value problems (IVPs) for ordinary diierential equations (ODEs), validated (also called interval) methods for IVPs for ODEs have two important advantages: if they return a solution to a problem, then (1) the problem is guaranteed to have a unique solution, and (2) an enclosure of the true solution is(More)
Compared to standard numerical methods for initial value problems (IVPs) for ordinary diierential equations (ODEs), validated methods for IVPs for ODEs have two important advantages: if they return a solution to a problem, then (1) the problem is guaranteed to have a unique solution, and (2) an enclosure of the true solution is produced. The authors survey(More)
This paper is one of a series underpinning the authors' DAETS code for solving DAE initial value problems by Taylor series expansion. First, building on the second author's structural analysis of DAEs (BIT 41 (2001) 364–394), it describes and justifies the method used in DAETS to compute Taylor coefficients (TCs) using automatic differentiation. The DAE may(More)
The numerical solution of initial value problems (IVPs) for ODEs is one of the fundamental problems in computation. Today, there are many well-established algorithms for solving IVPs. However, traditional integration methods usually provide only approximate values for the solution. Precise error bounds are rarely available. The error estimates, which are(More)
We propose a probabilistic graphical model (PGM) for prognosis and diagnosis of breast cancer. PGMs are suitable for building predictive models in medical applications, as they are powerful tools for making decisions under uncertainty from big data with missing attributes and noisy evidence. Previous work relied mostly on clinical data to create a(More)