3
votes
1answer
68 views

I want to study Numerical linear algebra [closed]

Would you like to recommend a book to me? the proof is explicit and easy to understand is preferred.
0
votes
0answers
24 views

Reference Request: Matrix of a composition(sum) of two operators is the Kronecker product (sum) of the matrices of each operator

Here is link to an example: http://en.wikipedia.org/wiki/Kronecker_sum_of_discrete_Laplacians, but it provides no references. Hoffman and Kunze(Linear Algebra) develop linear algebra with explicit ...
1
vote
1answer
47 views

References for numerical stochastic differential equations

I am currently working on a topic in physics which requires me to solve stochastic differential equations (specifically stoch. Schrödinger equation). I am a physicist and have not had any ...
0
votes
0answers
82 views

What is “kick back argument”?

I'm from Chile, and english isn't my natural language. I read in a many papers of Numerical Analysis the expression " using kick back argument" but I don't understand what means. I will appreciate ...
2
votes
0answers
30 views

Accurate computation of arcsec near branch points

The direct numerical implementations of the usual definitions of the complex $\mathrm{arcsec}(z)=\arccos(1/z)$ and similar for $\mathrm{arccsc}(z), \mathrm{arcsech}(z), $ etc are not accurate near ...
0
votes
0answers
11 views

About a theorem by Faber in interpolation theory

I am looking for a proof of this theorem: For any table of nodes there is a continuous function $f$ on an interval $[a,b]$ for which the sequence of interpolating polynomials diverges on $[a,b]$. ...
0
votes
1answer
64 views

Compare these two numerical analysis books ? Kincaid vs Quarteroni

I am considering to buy a reference books for using along side with my professors' notes in the graduate level numerical analysis. Which one is better ? Quarteroni's Numerical Mathematics Kincaid's ...
3
votes
1answer
78 views

Fermat-quotient of “order” 3: I found $68^{112} \equiv 1 \pmod {113^3}$ - are there bigger examples known?

I'm rereading an older text on fermat-quotients (see wikipedia) from which I have now the Question for $$ b^{p-1} \equiv 1 \pmod{ p^m} \qquad \text{ with $p \in \mathbb P $, $1 \lt b \lt p$ and ...
3
votes
0answers
35 views

Finite Difference Methods for arbitrary elliptic PDE

I am looking for textbook references that describe lattice numerical methods for arbitrary elliptic PDEs, particularly finite difference schemes and particularly in 2d. The few references that I have ...
1
vote
0answers
36 views

Literature investigating root finding of convex Functions

I am interested in using a result about Newton's method, which basically states that if f is convex on $[a,b]$ and it holds $f(a)<0$ and $f(b)>0$, then the Newton iteration converges to ...
0
votes
0answers
36 views

Finding zero of nonlinear function

I have a function $g(x)$ and would like to numerically find all the zeros of the function for $x$ in some interval $[a ,b]$. My function $g$ is nonlinear and discontinuous. I can compute the ...
2
votes
1answer
124 views

Numerical Solution of difference equation

I am trying to solve a nonlinear difference equation of the form: $x_{i+1} = f(x_i, x_{i-1})$ for $i = 0,\ldots,N-1$ with given boundary conditions $x_0 = a$ and $x_N = g(x_{N-1})$ where $f$ and $g$ ...
1
vote
0answers
57 views

A method called “incorrect method”

Good night. Is there a method called "incorrect method" to calculate second order differential equations? If so, please, is there a web page about it, as I have to investigate this method? Thank ...
2
votes
1answer
109 views

Solving Hamilton-Jacobi-Bellman equations numerically?

I've been told that HJB equations can be solved numerically. I know very little about the subject, could someone provide a couple of comments or a reference (ideally, one that is accessible for a ...
1
vote
1answer
50 views

Taking a linear operator inside an integral

I am currently reading up on the Newton iteration, and have come across a step in a proof that I don't understand, and am having difficulty finding in a numerical analysis textbook (as I don't know if ...
3
votes
2answers
68 views

what is name of this numerical scheme for ode?

Let's have system of ODEs $$ \dot x(t) = A(t)x(t) $$ I came up with this numerical scheme: $$ x_{n+1} = e^{\frac{h}{2}A(t_{n+1})}e^{\frac{h}{2}A(t_n)}x_n $$ where $h$ is time step, $t_n = nh$ and ...
1
vote
1answer
70 views

Prime numbers and limit(?)

Can someone help me to prove the following: $$\lim_{x\to\infty}(\sum_{p\leq x}\frac{1}{p}-\log(\log(x)) -C)=0$$ Where $C$ is a proper constant. Thank you...
4
votes
0answers
156 views

Test for equivalence of algebraic expressions

We are looking for the most efficient (most recent, or best) techniques to check if two algebraic expressions (elementary, Calculus-type functions) are equivalent (or if an expression is equivalent to ...
0
votes
0answers
40 views

Estimate a level set of the form $A \equiv \{\mathbf{x} \mid f(\mathbf{x})=\alpha \}$

Suppose I have a continuous function $f(\mathbf{x}):\mathbb{R}^d \mapsto\mathbb{R}$. I am interested in the level set $A \equiv \{\mathbf{x} \mid f(\mathbf{x})=\alpha \}$. Suppose the lebesgue measure ...
2
votes
1answer
1k views

Numerically solving a system of nonlinear ODEs with boundary conditions

I have a system of 6 second-order nonlinear ODEs involving 5 different functions of a variable $t$. Every function has a boundary condition at $0$. I've never taken a differential equations class and ...
1
vote
1answer
46 views

Numerical solutions to wave equation

Does the wave equation always have an analytical solution given well-behaved boundary/initial conditions? If not, under what conditions does the wave equation need to be solved numerically? This ...
1
vote
1answer
118 views

Diffusion Advection equation discretization scheme

I am looking for a good reference to understand the basic discretization schemes applied to the Stationary Diffusion Advection equation. $$-\epsilon \frac{d^2u(x)}{dx^2}+\beta \frac{du(x)}{dx}=0$$ ...
2
votes
2answers
81 views

Recommendations for website/journal/magazine in applied mathematics

Which website/journal/magazine would you recommend to keep up with advances in applied mathematics? More specifically my interest are: multivariate/spatial interpolation numerical methods ...
1
vote
2answers
467 views

Error estimation for spline interpolation

Can you please indicate a reference for the proof of the fact that the error when interpolating a $C^4$ function by a cubic spline is bounded by $Ch^4\sup_{[x_{i},x_{i+1}]} |f''''(x)|$?
1
vote
2answers
206 views

resources to study PDE from

I am an undergrad engineering student. I recently completed my second year, with that said, I have taken several calculus courses. Most recently I completed differential equations and multivariable ...
3
votes
1answer
107 views

About iterative refinement to the solution of the linear equations

I want to know what is iterative refinement for improving the solution to the linear equations? How they improve solutions and what are the various techniques for the iterative refinements? Any ...
2
votes
1answer
80 views

Reference request: Newton-Kantorovich hypothesis for polynomials of integral coefficients

Kantorovich's theorem states that the Newton method for finding the roots of a nonlinear function is guaranteed to converge if a parameter $h$, determined by the values of the function and its ...
0
votes
1answer
54 views

Can anyone recommend me a good pdf link to learn B-spline with a lot of examples?

I really hope someone can recommend me a good link to study B-spline with a lot of examples that I could grasp the concept very easily! Thanks! :)
4
votes
1answer
118 views

References on constrained least square problems?

I have met some constrained least square problems, for example, my last post. I found that there are various methods for slightly different constraints, and still I often had little clue about how to ...
3
votes
1answer
57 views

Books for mathematics used in computer games.

I'm looking for a good book (idiot proof) for learning all the magic behind computing matrices, quaternions, euler angles, orientation in 3d space and more... Book needs to have examples and ...
1
vote
0answers
169 views

Reference for Finite Difference Schemes

Is there any place that I can find a list of different PDEs and common finite difference schemes used for each? I have seen tables of finite difference coefficients such as the one here ...
0
votes
3answers
313 views

Book in Numerical analysis

What books are good an introductory course in Numerical analysis? I look for a book with many applications, especially in biology
4
votes
2answers
98 views

Linear regression where undershooting isn't as bad as overshooting

Given a set of points $(x_i, y_i)$, least-squares linear regression finds the linear function $L$ such that $$\sum \varepsilon(y_i, L(x_i))$$ is minimized, where $\varepsilon(y, y') = (y-y')^2$ is the ...
1
vote
2answers
383 views

GMRES algorithm

Can you suggest me a reference (besides Wikipedia) where the GMRES (Generalized minimal residual method) algorithm is explained in full detail, in a nice and easy way to understand? A clearly written, ...
2
votes
1answer
133 views

Book on constrained numerical optimization

For unconstrained numerical optimization I have been using the book "Numerical Methods for Unconstrained Optimization and Nonlinear Equations" by Dennis and Schnabel. I found it to be a great book ...
2
votes
1answer
571 views

Numerical methods book

I'm looking for an introductory book on numerical methods. I'm beginning to learn to program (in Haskell, a functional language, if that would affect the recommendations). The reason I want such a ...
1
vote
1answer
283 views

Spline Theory and Code

On P. Janert's book Data Analysis with Open Source Tools there is a discussion on splines, that they are "constructed from piecewise polynomial functions (typically cubic) that are joined together in ...
3
votes
1answer
101 views

What is a good, easy to read book that tells you how to make series converge over a longer interval?

I've read that there are methods called series accelerations or sequence transformations that can help you make some divergent series converge and convergent series converge over a longer interval. I ...
1
vote
1answer
52 views

How to construct a polynomial with minimum deviation from zero on the complex region?

I need to compute the analog of Chebyshev polynomials (which give the minimum deviation from zero on [-1,1]) on the given region $\Omega\subset \mathbb C$. More precisely: find $P_n$ such that ...
3
votes
1answer
782 views

Numerical solving a constrained system of differential equation

I am in trouble on finding a numerical technique to solve the following system of equations $$\ddot q_1(t)=f_1(q_1(t),q_2(t))$$ $$\ddot q_2(t)=f_2(q_1(t),q_2(t))$$ with a constrain of the kind: ...
1
vote
0answers
60 views

reference request

Can anybody help me to find the books on numerical solutions of partial differential equations including examples on irregular geometry (specially books or links on matlab code examples in this case)? ...
1
vote
0answers
270 views

Second order central difference of the Nth order

I'm trying to find some tabulated data in some big-and-smart-book with regards to second order central difference of a function of just one variable: f''(x). I did find formula for 7th order [1], but ...
1
vote
2answers
106 views

High order methods for solving ODEs

I would like to know about really high order methods for solving ODEs. Say of order 30 and higher. What are they? Any surveys/reviews?
5
votes
1answer
364 views

How to use FEM to solve a PDE

I come from a Computer Science background and I've been around searching for a concise tutorial that tells me how Finite Element Method is used to solve a certain partial differential equation. ...
2
votes
1answer
185 views

Is $O(10^{-6})$ an acceptable notation in numerical analysis?

In mathematics, the big $O$ notation is used to describe the limiting behavior of a function. It is abuse of notation to say $$ f(x)=O(g(x)). $$ But this is understandable. However, in the class of ...
3
votes
3answers
280 views

Numerical Analysis References

Could anyone suggest any good (perhaps online ref papers) reference material on numerical analysis focusing on determining accuracy/estimated errors, rates/orders of convergence especially when ...
5
votes
0answers
1k views

Restricted Three-Body Problem

The movement of a spacecraft between Earth and the Moon is an example of the infamous Three Body Problem. It is said that a general analytical solution for TBP is not known because of the complexity ...
7
votes
1answer
291 views

PDE - Feynman-Kac vs. finite difference methods

I've heard that in greater than three dimensions, it's more efficient to solve a second-order parabolic PDE using a Monte-Carlo method based on the Feynman-Kac formula that it is to use finite ...
2
votes
3answers
232 views