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The Chebyshev polynomials form a complete orthogonal system. The Chebyshev series converges to f(x) if the function is piecewise smooth and continuous. The smoothness requirement can be relaxed in most cases – as long as there are a finite number of discontinuities in f(x) and its derivatives. At a discontinuity, the series will converge to ...
One can obtain polynomials very close to the optimal one by expanding the given function in terms of Chebyshev polynomials and then cutting off the expansion at the desired degree. This is similar to the Fourier analysis of the function, using the Chebyshev polynomials instead of the usual trigonometric functions.
Clenshaw–Curtis quadrature and Fejér quadrature are methods for numerical integration, or "quadrature", that are based on an expansion of the integrand in terms of Chebyshev polynomials. Equivalently, they employ a change of variables x = cos θ {\displaystyle x=\cos \theta } and use a discrete cosine transform (DCT) approximation for ...
The Gonda building was the largest building project in the Mayo Clinic's history, the Leslie & Susan Gonda Building was constructed in three phases to a height of 21 stories. A fourth phase is planned for completion in the 2020s. Located at the heart of the campus, Gonda is the centerpiece of Mayo's integrated practice.
The Mayo Clinic announced a $5 billion expansion plan for its flagship campus Tuesday that includes new buildings designed so they can evolve and expand as patient needs change over the coming ...
In its first three years, the CFI completed more than 100 innovation projects within the Mayo system, ranging from redesigning Mayo's traditional clinical exam room; to streamlining job descriptions and protocols in a dermatology clinic; to analyzing how hospital care teams hand off patients from one team to another; to supporting a project ...
Aug. 16—Mayo Clinic is expanding its proton beam therapy program by spending $200 million to build a new 110,000-square-foot facility in downtown Rochester. The announcement was made this ...
The Chebyshev pseudospectral method for optimal control problems is based on Chebyshev polynomials of the first kind. It is part of the larger theory of pseudospectral optimal control , a term coined by Ross . [ 1 ]