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Mar
14
comment Is linear algebra laying the foundation for something important?
@lisyarus, probably not "often", unless you deal with a lot of PDEs or networks. There's still much demand for dense methods, especially those that exploit structure. Nevertheless, linear algebra is one of the very handy tools in the box of a numericist.
Mar
14
revised Integral of $\int\frac{dx}{(x^4-1)^{3/2}}$
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Mar
14
revised How to prove the result of this definite integral?
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Mar
14
answered Solving $\ln{x}=\tan{x}$ with infinitely many solutions
Mar
14
answered How to prove the result of this definite integral?
Mar
14
answered Integral of $\int\frac{dx}{(x^4-1)^{3/2}}$
Mar
13
answered Circular Helicoid
Mar
13
comment How to tell what dimension an object is?
As a further complication, we have objects called "fractals" that feature a fractional dimension; the Koch snowflake has a dimension of $\approx 1.26186$, for instance.
Mar
13
comment Algorithm(s) for computing an elementary symmetric polynomial
@Thomas, a lower Hessenberg matrix like the one in this answer can be decomposed in $O(n^2)$ operations; the determinant is then easily obtained from the triangular factor. Have a look at "Hyman's method", for instance.
Mar
12
revised Cauchy Principal value of integral with undefined point
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Mar
11
revised Cauchy Principal value of integral with undefined point
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Mar
11
comment cubic root of negative numbers
The last bit is the only blemish in an otherwise excellent answer.
Mar
11
comment Cauchy Principal value of integral with undefined point
Yes, if you perform the series expansion of that integrand at $z=0$, you should see something like $-\frac1{50}-\frac{16z^2}{1875}+\cdots$.
Mar
11
revised Approximating hypergeometric function F(1,1+a,2+a,z) for z->1
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Mar
11
comment Cauchy Principal value of integral with undefined point
In principle, one could use a convergence acceleration method like Richardson extrapolation on the sequence generated in this manner, long as you pick an appropriate auxiliary sequence.
Mar
11
answered Cauchy Principal value of integral with undefined point
Mar
11
comment Cauchy Principal value of integral with undefined point
NIntegrate[] can handle it directly: NIntegrate[1/((z + 1)^2 + 4) 1/(Exp[-z] - 1), {z, -∞, 0, ∞}, Method -> PrincipalValue]
Mar
9
comment What is the intuitive relationship between SVD and PCA
@sv_jan5, if memory serves, Golub/Van Loan mention the Läuchli example. A number of other numerical linear algebra books will have this discussion and similar examples; look around.
Mar
8
comment What is the intuitive relationship between SVD and PCA
@sv_jan, did ya even try the example I gave, if you have to ask that?
Mar
6
comment Does anyone know a function that can describe a harmonic series?
You'll want to look up the digamma function.