| Budget Amount *help |
¥5,590,000 (Direct Cost: ¥4,300,000、Indirect Cost: ¥1,290,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2012: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
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| Outline of Final Research Achievements |
"Self-validating numerical computations" stands for a computer-assisted approach to prove the existence of the solutions and its guaranteed error bounds for a given problem. By using self-validating numerical computations, this reserch proposed a computer-assisted procedure to assure the invertibility of a linear operator which is the sum of an unbounded bijective and a bounded operator in a Hilbert space, and to compute a bound for the norm of its inverse. We also showed that our bounds are expected to converge to the exact operator norm and to provide accurate and efficient enclosure results for the solution of nonlinear problem by infinite-dimensional Newton-type methods.
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