Polynomials, Interpolation, and integralon
Polynomials, Interpolation, and integralon
...
118
17. Polynomials, Interpolation,
and Integration
Polynomial functions are frequently used by numerical
methods, and thus MATLAB provides several routines
that operate on polynomials and piece-wise ...
quad
and
quadl
must operate
on a vector
x
and return
f(x)
for each component of the
vector. An optional fourth argument to
quad
and
quadl
modifies the error...
Interpolation and Extrapolation part 3
... m and (the term R
(i+1) (i+m−1)
inequation 3.2.3) m−1 points. It is started
with
R
i
= y
i
(3.2.4)
and with
R ≡ [R
i(i+1) (i+m)
with m = −1] = 0 (3.2.5)
Now, exactly as in equations (3.1.4) and ... ya[], int n, float x, float *y, float *dy)
Given arrays
xa[1 n]
and
ya[1 n]
, and given a value of
x
, this routine returns a value of
y
and an accuracy estimate
dy
. The value returned...
Interpolation and Extrapolation part 4
... (3.3.3) and
(3.3.4) is entirely through the linear x-dependence of A and B, and (through A and
B) the cubic x-dependence of C and D.
We can readily check that y
is in fact the second derivative ... sequential calls to this
routine are at random values of x. If sequential calls
are in order, and closely spaced, one would do better
tostorepreviousvaluesofklo and khi and test...
Interpolation and Extrapolation part 5
... monotonically decreasing, and
given a number x, find an integer j such that x lies between xx[j] and xx[j+1].
For this task, let us define fictitious array elements xx[0] and xx[n+1] equal to
plus ... much shorter xx and yy
arrays, of length m. How do you make the connection?
The solution: Calculate
k = IMIN(IMAX(j-(m-1)/2,1),n+1-m)
(The macros IMIN and IMAX give the minimum and maxi...
Interpolation and Extrapolation part 6
... coefficients can be accurately and stably
determined even in the presence of statistical errors in the tabulated values. (See
§14.8.) Interpolation, where the number of coefficients and number of tabulated
pointsare ... c
0
from the y
i
’s and divide each by its corresponding x
i
. Throwing
out one point (the one with smallest x
i
is a good candidate), we can repeat the
procedure to find...
Interpolation and Extrapolation part 7
... arrays
x1a[1 m]
and
x2a[1 n]
of independent variables, and a submatrix of function
values
ya[1 m][1 n]
, tabulated at the grid points defined by
x1a
and
x2a
; and given values
x1
and
x2
of the independent ... gra-
dients, and cross derivative at the four grid points of a rectangular grid cell (numbered coun-
terclockwise from the lower left), and given
d1
and
d2
, the length of...
Tài liệu Interpolation and Extrapolation part 1 pptx
... (§3.2). Trigonometric functions, sines and cosines, give
rise to trigonometric interpolation and related Fourier methods, which we defer to
Chapters 12 and 13.
There is an extensive mathematical ... arbitrary x by, in some sense, drawing a
smooth curve through (and perhaps beyond) the x
i
. If the desired x is in between the
largest and smallest of the x
i
’s, the problem is called i...
Tài liệu Interpolation and Extrapolation part 2 doc
... REFERENCES AND FURTHER READING:
Abramowitz, M., and Stegun, I.A. 1964,
Handbook of Mathematical Functions
, Applied Mathe-
matics Series, Volume 55 (Washington: National Bureau of Standards; reprinted ... REFERENCES AND FURTHER READING:
Abramowitz, M., and Stegun, I.A. 1964,
Handbook of Mathematical Functions
, Applied Mathe-
matics Series, Volume 55 (Washington: National Bureau of St...
Báo cáo khoa học: "Integrating history-length interpolation and classes in language modeling" pdf
... engines. In Michael Grimm and Kris-
tian Kroschel, editors, Robust Speech Recognition and
Understanding, pages 301–318. I-Tech Education and
Publishing.
Imed Zitouni and Qiru Zhou. 2008. Hierarchical ... op-
posed to classes) (Whittaker and Woodland, 2001;
Emami and Jelinek, 2005; Uszkoreit and Brants,
2008). In this work, we use the Brown type of
model: it is simpler and has...
Từ khóa:
- differences interpolation and numerical differentiation
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- lfos interpolation and trackballs to move stuff
- polynomials and transcendental entire functions
- on the computational complexity of the jones and tutte polynomials
- curve fitting and interpolation
- polynomials of maps and matrices
- polynomials product forms and continued fractions
- polynomials taylor series and power series